![2-8 Advanced Signal Processing Handbook
FIGURE 2.4 Triangular systolic array.
them are characterized by an impulse response of finite duration. In other words, they are examples of
a finite-duration impulse response (FIR) filter, whose structures contain feedforward paths only. On the
other hand, the filter structure shown in Figure 2.5 is an example of an infinite-duration impulse response
(HR) filter. The feature that distinguishes an HR filter from an FIR filter is the inclusion o f feedback paths.
Indeed, it is the presence of feedback that makes the duration of the impulse response of an HR filter
infinitely long. Furthermore, the presence of feedback introduces a new problem, namely, that of stability.
In particular, it is possible for an IIR filter to become unstable (i.e., break into oscillation), unless special
precaution is taken in the choice of feedback coefficients. By contrast, an FIR filter in inherently stable.
This explains the reason for the popular use of FIR filters, in one form or another, as the structural basis
for the design of linear adaptive filters.
2.4 Approaches to the Development of Linear
Adaptive Filtering Algorithms
There is no unique solution to the linear adaptive filtering problem. Rather, we have a “kit of tools”
represented by a variety of recursive algorithms, each of which offers desirable features of its own. (For
complete detailed treatment of linear adaptive filters, see the book by Haykin [1996].) The challenge
facing the user of adaptive filtering is (1) to understand the capabilities and limitations of various adaptive
filtering algorithms and (2) to use this understanding in the selection of the appropriate algorithm for
the application at hand.
Basically, we may identify two distinct approaches for deriving recursive algorithms for the operation
of linear adaptive filters, as discussed next.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-53-320.jpg)
![him: Martin had known all about Burr's criminal enterprise. Jefferson
had received a letter from Baltimore stating that this had been
believed generally in that city "for more than a twelve-month." Let
Hay subpœna as a witness the writer of this letter—one Greybell.
Something must be done to "put down" the troublesome "bull-
dog": "Shall L M be summoned as a witness against Burr?" Or "shall
we move to commit L M as particeps criminis with Burr? Greybell will
fix upon him misprision of treason at least ... and add another proof
that the most clamorous defenders of Burr are all his accomplices."
As for Bollmann! "If [he] finally rejects his pardon, & the Judge
decides it to have no effect ... move to commit him immediately for
treason or misdemeanor."[1122] But Bollmann, in open court, had
refused Jefferson's pardon six days before the President's vindictively
emotional letter was written.
After Marshall delivered his opinion on the question of the
subpœna to Jefferson, Burr insisted, in an argument as convincing
as it was brief, that the Chief Justice should now deliver the
supplementary charge to the grand jury as to what evidence it could
legally consider. Marshall announced that he would do so on the
following Monday.[1123]
Several witnesses for the Government were sworn, among them
Commodore Thomas Truxtun, Commodore Stephen Decatur, and
"General" William Eaton. When Dr. Erich Bollmann was called to the
book, Hay stopped the administration of the oath. Bollmann had told
the Government all about Burr's "plans, designs and views," said the
District Attorney; "as these communications might criminate doctor
Bollman before the grand jury, the president has communicated to
me this pardon"—and Hay held out the shameful document. He had
already offered it to Bollmann, he informed Marshall, but that
incomprehensible person would neither accept nor reject it. His
evidence was "extremely material"; the pardon would "completely
exonerate him from all the penalties of the law." And so, exclaimed
Hay, "in the presence of this court, I offer this pardon to him, and if](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-56-320.jpg)
!["I have already answered that question several times. I say no,"
responded Bollmann. "I repeat, that I would have refused it before,
but that I wished this opportunity of publicly declaring it."[1124]
Bollmann was represented by an attorney of his own, a Mr.
Williams, who now cited an immense array of authorities on the
various questions involved. Counsel on both sides entered into the
discussion. One "reason why doctor Bollman has refused this
pardon" was, said Martin, "that it would be considered as an
admission of guilt." But "doctor Bollman does not admit that he has
been guilty. He does not consider a pardon as necessary for an
innocent man. Doctor Bollman, sir, knows what he has to fear from
the persecution of an angry government; but he will brave it all."
Yes! cried Martin, with immense effect on the excited spectators,
"the man, who did so much to rescue the marquis la Fayette from
his imprisonment, and who has been known at so many courts,
bears too great a regard for his reputation, to wish to have it
sounded throughout Europe, that he was compelled to abandon his
honour through a fear of unjust persecution." Finally the true-
hearted and defiant Bollmann was sent to the grand jury without
having accepted the pardon, and without the legal effect of its offer
having been decided.[1125]
When the Richmond Enquirer, containing Marshall's opinion on the
issuance of the subpœna duces tecum, reached Washington, the
President wrote to Hay an answer of great ability, in which Jefferson
the lawyer shines brilliantly forth: "As is usual where an opinion is to
be supported, right or wrong, he [Marshall] dwells much on smaller
objections, and passes over those which are solid.... He admits no
exception" to the rule "that all persons owe obedience to subpœnas
... unless it can be produced in his law books."
"But," argues Jefferson, "if the Constitution enjoins on a particular
officer to be always engaged in a particular set of duties imposed on
him, does not this supersede the general law, subjecting him to
minor duties inconsistent with these? The Constitution enjoins his](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-58-320.jpg)
![[the President's] constant agency in the concerns of 6. millions of
people. Is the law paramount to this, which calls on him on behalf of
a single one?"
Let Marshall smoke his own tobacco: suppose the Sheriff of
Henrico County should summon the Chief Justice to help "quell a
riot"? Under the "general law" he is "a part of the posse of the State
sheriff"; yet, "would the Judge abandon major duties to perform
lesser ones?" Or, imagine that a court in the most distant territory of
the United States "commands, by subpœnas, the attendance of all
the judges of the Supreme Court. Would they abandon their posts as
judges, and the interests of millions committed to them, to serve the
purposes of a single individual?"
The Judiciary was incessantly proclaiming its "independence," and
asserting that "the leading principle of our Constitution is the
independence of the Legislature, executive and judiciary of each
other." But where would be such independence, if the President
"were subject to the commands of the latter, & to imprisonment for
disobedience; if the several courts could bandy him from pillar to
post, keep him constantly trudging from north to south & east to
west, and withdraw him entirely from his constitutional duties?"
Jefferson vigorously resented Marshall's personal reference to him.
"If he alludes to our annual retirement from the seat of government,
during the sickly season," Hay ought to tell Marshall that Jefferson
carried on his Executive duties at Monticello.[1126]
Crowded with sensations as the proceedings had been from the
first, they now reached a stage of thrilling movement and high color.
The long-awaited and much-discussed Wilkinson had at last arrived
"with ten witnesses, eight of them Burr's select men," as Hay
gleefully reported to Jefferson.[1127] Fully attired in the showy
uniform of the period, to the last item of martial decoration, the fat,
pompous Commanding General of the American armies strode
through the crowded streets of Richmond and made his way among](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-59-320.jpg)
![the awed and gaping throng to his seat by the side of the
Government's attorneys.
Washington Irving reports that "Wilkinson strutted into the Court,
and ... stood for a moment swelling like a turkey cock." Burr ignored
him until Marshall "directed the clerk to swear General Wilkinson; at
the mention of the name Burr turned his head, looked him full in the
face with one of his piercing regards, swept his eye over his whole
person from head to foot, as if to scan its dimensions, and then
coolly ... went on conversing with his counsel as tranquilly as ever."
[1128]
Wilkinson delighted Jefferson with a different description: "I
saluted the Bench & in spite of myself my Eyes darted a flash of
indignation at the little Traitor, on whom they continued fixed until I
was called to the Book—here Sir I found my expectations verified—
This Lyon hearted Eagle Eyed Hero, sinking under the weight of
conscious guilt, with haggard Eye, made an Effort to meet the
indignant salutation of outraged Honor, but it was in vain, his
audacity failed Him, He averted his face, grew pale & affected
passion to conceal his perturbation."[1129]
But the countenance of a thin, long-faced, roughly garbed man
sitting among the waiting witnesses was not composed when
Wilkinson appeared. For three weeks Andrew Jackson to all whom
he met had been expressing his opinion of Wilkinson in the
unrestrained language of the fighting frontiersman;[1130] and he
now fiercely gazed upon the creature whom he regarded as a triple
traitor, his own face furious with scorn and loathing.
Within the bar also sat that brave and noble man whose career of
unbroken victories had made the most brilliant and honorable page
thus far in the record of the American Navy—Commodore Thomas
Truxtun. He was dressed in civilian attire.[1131] By his side, clad as a
man of business, sat a brother naval hero of the old days,
Commodore Stephen Decatur.[1132] A third of the group was](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-60-320.jpg)
![Benjamin Stoddert, the Secretary of the Navy under President
Adams.[1133]
In striking contrast with the dignified appearance and modest
deportment of these gray-haired friends was the gaudily appareled,
aggressive mannered Eaton, his restlessness and his complexion
advertising those excesses which were already disgusting even the
hard-drinking men then gathered in Richmond. Dozens of
inconspicuous witnesses found humbler places in the audience,
among them Sergeant Jacob Dunbaugh, bearing himself with
mingled bravado, insolence, and humility, the stripes on the sleeve
of his uniform designating the position to which Wilkinson had
restored him.
Dunbaugh had gone before the grand jury on Saturday, as had
Bollmann; and now, one by one, Truxtun, Decatur, Eaton, and others
were sent to testify before that body.
Eaton told the grand jury the same tale related in his now famous
affidavit.[1134]
Commodore Truxtun testified to facts as different from the
statements made by "the hero of Derne"[1135] as though Burr had
been two utterly contrasted persons. During the same period that
Burr had seen Eaton, he had also conversed with him, said Truxtun.
Burr mentioned a great Western land speculation, the digging of a
canal, and the building of a bridge. Later on Burr had told him that
"in the event of a war with Spain, which he thought inevitable, ... he
contemplated an expedition to Mexico," and had asked Truxtun "if
the Havanna could be easily taken ... and what would be the best
mode of attacking Carthagena and La Vera Cruz by land and sea."
The Commodore had given Burr his opinion "very freely," part of it
being that "it would require a naval force." Burr had answered that
"that might be obtained," and had frankly asked Truxtun if he "would
take the command of a naval expedition."](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-61-320.jpg)
!["I asked him," testified Truxtun, "if the executive of the United
States were privy to, or concerned in the project? He answered
emphatically that he was not: ... I told Mr. Burr that I would have
nothing to do with it.... He observed to me, that in the event of a
war [with Spain], he intended to establish an independent
government in Mexico; that Wilkinson, the army, and many officers
of the navy would join.... Wilkinson had projected the expedition,
and he had matured it; that many greater men than Wilkinson would
join, and that thousands to the westward would join."
In some of the conversations "Burr mentioned to me that the
government was weak," testified Truxtun, "and he wished me to get
the navy of the United States out of my head;[1136] ... and not to
think more of those men at Washington; that he wished to see or
make me, (I do not recollect which of those two terms he used) an
Admiral."
Burr wished Truxtun to write to Wilkinson, to whom he was about
to dispatch couriers, but Truxtun declined, as he "had no subject to
write about." Again Burr urged Truxtun to join the enterprise
—"several officers would be pleased at being put under my
command.... The expedition could not fail—the Mexicans were ripe
for revolt." Burr "was sanguine there would be war," but "if he was
disappointed as to the event of war, he was about to complete a
contract for a large quantity of land on the Washita; that he
intended to invite his friends to settle it; that in one year he would
have a thousand families of respectable and fashionable people, and
some of them of considerable property; that it was a fine country,
and that they would have a charming society, and in two years he
would have doubled the number of settlers; and being on the
frontier, he would be ready to move whenever a war took place....
"All his conversations respecting military and naval subjects, and
the Mexican expedition, were in the event of a war with Spain."
Truxtun testified that he and Burr were "very intimate"; that Burr](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-62-320.jpg)
![talked to him with "no reserve"; and that he "never heard [Burr]
speak of a division of the union."
Burr had shown Truxtun the plan of a "kind of boat that plies
between Paulus-Hook and New-York," and had asked whether such
craft would do for the Mississippi River and its tributaries, especially
on voyages upstream. Truxtun had said they would. Burr had asked
him to give the plans to "a naval constructor to make several
copies," and Truxtun had done so. Burr explained that "he intended
those boats for the conveyance of agricultural products to market at
New-Orleans, and in the event of war [with Spain], for transports."
The Commodore testified that Burr made no proposition to invade
Mexico "whether there was war [with Spain] or not." He was so sure
that Burr meant to settle the Washita lands that he was "astonished"
at the newspaper accounts of Burr's treasonable designs after he
had gone to the Western country for the second time.
Truxtun had freely complained of what amounted to his discharge
from the Navy, being "pretty full" himself of "resentment against the
Government," and Burr "joined [him] in opinion" on the
Administration.[1137]
Jacob Dunbaugh told a weird tale. At Fort Massac he had been
under Captain Bissel and in touch with Burr. His superior officer had
granted him a furlough to accompany Burr for twenty days. Before
leaving, Captain Bissel had "sent for [Dunbaugh] to his quarters,"
told him to keep "any secrets" Burr had confided to him, and
"advised" him "never to forsake Col. Burr"; and "at the same time he
made [Dunbaugh] a present of a silver breast plate."
After Dunbaugh had joined the expedition, Burr had tried to
persuade him to get "ten or twelve of the best men" among his
nineteen fellow soldiers then at Chickasaw Bluffs to desert and join
the expedition; but the virtuous sergeant had refused. Then Burr
had asked him to "steal from the garrison arms such as muskets,
fusees and rifles," but Dunbaugh had also declined this reasonable](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-63-320.jpg)
![request. As soon as Burr learned of Wilkinson's action, he told
Dunbaugh to come ashore with him armed "with a rifle," and to
"conceal a bayonet under [his] clothes.... He told me he was going
to tell me something I must never relate again, ... that General
Wilkinson had betrayed him ... that he had played the devil with
him, and had proved the greatest traitor on the earth."
Just before the militia broke up the expedition, Burr and Wylie, his
secretary, got "an axe, auger and saw," and "went into Colonel
Burr's private room and began to chop," Burr first having "ordered
no person to go out." Dunbaugh did go out, however, and "got on
the top of the boat." When the chopping ceased, he saw that "a Mr.
Pryor and a Mr. Tooly got out of the window," and "saw two bundles
of arms tied up with cords, and sunk by cords going through the
holes at the gunwales of Colonel Burr's boat." The vigilant Dunbaugh
also saw "about forty or forty-three stands [of arms], besides pistols,
swords, blunderbusses, fusees, and tomahawks"; and there were
bayonets too.[1138]
Next Wilkinson detailed to the grand jury the revelations he had
made to Jefferson. He produced Burr's cipher letter to him, and was
forced to admit that he had left out the opening sentence of it
—"Yours, postmarked 13th of May, is received"—and that he had
erased some words of it and substituted others. He recounted the
alarming disclosures he had so cunningly extracted from Burr's
messenger, and enlarged upon the heroic measures he had taken to
crush treason and capture traitors. For four days[1139] Wilkinson
held forth, and himself escaped indictment by the narrow margin of
7 to 9 of the sixteen grand jurymen. All the jurymen, however,
appear to have believed him to be a scoundrel.[1140]
"The mammoth of iniquity escaped," wrote John Randolph in acrid
disgust, "not that any man pretended to think him innocent, but
upon certain wire-drawn distinctions that I will not pester you with.
Wilkinson is the only man I ever saw who was from the bark to the
very core a villain.... Perhaps you never saw human nature in so](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-64-320.jpg)
![degraded a situation as in the person of Wilkinson before the grand
jury, and yet this man stands on the very summit and pinnacle of
executive favor."[1141]
Samuel Swartwout, the courier who had delivered Burr's ill-fated
letter, "most positively denied" that he had made the revelations
which Wilkinson claimed to have drawn from him.[1142] The youthful
Swartwout as deeply impressed the grand jury with his honesty and
truthfulness as Wilkinson impressed that body with his
untrustworthiness and duplicity.[1143]
Peter Taylor and Jacob Allbright then recounted their experiences.
[1144] And the Morgans told of Burr's visit and of their inferences
from his mysterious tones of voice, glances of eye, and cryptic
expressions. So it was, that in spite of overwhelming testimony of
other witnesses,[1145] who swore that Burr's purposes were to settle
the Washita lands and in the event of war with Spain, and only in
that event, to invade Mexico, with never an intimation of any project
hostile to the United States—so it was that bills of indictment for
treason and for misdemeanor were, on June 24, found against Aaron
Burr of New York and Harman Blennerhassett of Virginia. The
indictment for treason charged that on December 13, 1806, at
Blennerhassett's island in Virginia, they had levied war on the United
States; and the one for misdemeanor alleged that, at the same time
and place, they had set on foot an armed expedition against territory
belonging to His Catholic Majesty, Charles IV of Spain.[1146]
This result of the grand jury's investigations was reached because
of that body's misunderstanding of Marshall's charge and of his
opinion in the Bollmann and Swartwout case.[1147]
John Randolph, as foreman of the grand jury, his nose close to the
ground on the scent of the principal culprit, came into court the day
after the indictment of Burr and Blennerhassett and asked for the
letter from Wilkinson to Burr, referred to in Burr's cipher dispatch to
Wilkinson, and now in the possession of the accused. Randolph said](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-65-320.jpg)
![that, of course, the grand jury could not ask Burr to appear before
them as a witness, but that they did want the letter.
Marshall declared "that the grand jury were perfectly right in the
opinion." Burr said that he could not reveal a confidential
communication, unless "the extremity of circumstances might impel
him to such a conduct." He could not, for the moment, decide; but
that "unless it were extorted from him by law" he could not even
"deliberate on the proposition to deliver up any thing which had
been confided to his honour."
Marshall announced that there was no "objection to the grand jury
calling before them and examining any man ... who laid under an
indictment." Martin agreed "there could be no objection."
The grand jury did not want Burr as a witness, said John
Randolph. They asked only for the letter. If they should wish Burr's
presence at all, it would be only for the purpose of identifying it. So
the grand jury withdrew.[1148]
Hay was swift to tell his superior all about it, although he trembled
between gratification and alarm. "If every trial were to be like that, I
am doubtful whether my patience will sustain me while I am wading
thro' this abyss of human depravity."
Dutifully he informed the President that he feared that "the Gr:
Jury had not dismissed all their suspicions of Wilkinson," for John
Randolph had asked for his cipher letter to Burr. Then he described
to Jefferson the intolerable prisoner's conduct: "Burr rose
immediately, & declared that no consideration, no calamity, no
desperation, should induce him to betray a letter confidentially
written. He could not even allow himself to deliberate on a point,
where his conduct was prescribed by the clearest principles of honor
&c. &c. &c."
Hay then related what Marshall and John Randolph had said,
underscoring the statement that "the Gr: Jury did not want A. B. as
a witness." Hay did full credit, however, to Burr's appearance of](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-66-320.jpg)
![candor: "The attitude & tone assumed by Burr struck everybody.
There was an appearance of honor and magnanimity which
brightened the countenances of the phalanx who daily attend, for his
encouragement & support."[1149]
Day after day was consumed in argument on points of evidence,
while the grand jury were examining witnesses. Marshall delivered a
long written opinion upon the question as to whether a witness
could be forced to give testimony which he believed might criminate
himself. The District Attorney read Jefferson's two letters upon the
subject of the subpœna duces tecum. No pretext was too fragile to
be seized by one side or the other, as the occasion for argument
upon it demanded—for instance, whether or not the District Attorney
might send interrogatories to the grand jury. Always the lawyers
spoke to the crowd as well as to the court, and their passages at
arms became ever sharper.[1150]
Wilkinson is "an honest man and a patriot"—no! he is a liar and a
thief; Louisiana is a "poor, unfortunate, enslaved country"; letters
had been seized by "foulness and violence"; the arguments of Burr's
attorneys are "mere declamations"; the Government's agents are
striving to prevent Burr from having "a fair trial ... the newspapers
and party writers are employed to cry and write him down; his
counsel are denounced for daring to defend him; the passions of the
grand jury are endeavored to be excited against him, at all events";
[1151] Hay's mind is "harder than Ajax's seven fold shield of bull's
hide"; Edmund Randolph came into court "with mysterious looks of
awe and terror ... as if he had something to communicate which was
too horrible to be told"; Hay is always "on his heroics"; he "hopped
up like a parched pea"; the object of Burr's counsel is "to prejudice
the surrounding multitude against General Wilkinson"; one
newspaper tale is "as impudent a falsehood as ever malignity had
uttered"—such was the language with which the arguments were
adorned. They were, however, well sprinkled with citations of
authority.[1152]](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-67-320.jpg)
![FOOTNOTES:
[1017] See vol. i, 201, of this work.
[1018] Tobacco chewing and smoking in court-rooms continued
in most American communities in the South and West down to a
very recent period.
[1019] Address of John Tyler on "Richmond and its Memories,"
Tyler, i, 219.
[1020] Irving was twenty-four years old when he reported the
Burr trial.
[1021] Blennerhassett Papers: Safford, 465. Marshall made this
avowal to Luther Martin, who personally told Blennerhassett of it.
[1022] Judge Francis M. Finch, in Dillon, i, 402.
"The men who framed that instrument [Constitution]
remembered the crimes that had been perpetrated under the
pretence of justice; for the most part they had been traitors
themselves, and having risked their necks under the law they
feared despotism and arbitrary power more than they feared
treason." (Adams: U.S. iii, 468.)
[1023] A favorite order from the bench for the execution of the
condemned was that the culprit should be drawn prostrate at the
tails of horses through the jagged and filthy streets from the
court-room to the place of execution; the legs, arms, nose, and
ears there cut off; the intestines ripped out and burned "before
the eyes" of the victim; and finally the head cut off. Details still
more shocking were frequently added. See sentences upon
William, Lord Russell, July 14, 1683 (State Trials Richard II to
George I, vol. 3, 660); upon Algernon Sidney, November 26, 1683
(ib. 738); upon William, Viscount Stafford, December 7, 1680 (ib.
214); upon William Stayley, November 21, 1678 (ib. vol. 2, 656);
and upon other men condemned for treason.
[1024] Even in Philadelphia, after the British evacuation of that
place during the Revolution, hundreds were tried for treason.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-68-320.jpg)
![Lewis alone, although then a very young lawyer, defended one
hundred and fifty-two persons. (See Chase Trial, 21.)
[1025] "In the English law ... the rule ... had been that enough
heads must be cut off to glut the vengeance of the Crown."
(Isaac N. Phillips, in Dillon, ii, 394.)
[1026] Iredell's charge to the Georgia Grand Jury, April 26,
1792, Iredell: McRee, ii, 349; and see Iredell's charge to the
Massachusetts Grand Jury, Oct. 12, 1792, ib. 365.
[1027] See his concurrence with Judge Peters's charge in the
Fries case, Wharton: State Trials, 587-91; and Peters's opinion, ib.
586; also see Chase's charge at the second trial of Fries, ib. 636.
[1028] "The President's popularity is unbounded, and his will is
that of the nation.... Such is our present infatuation." (Nicholson
to Randolph, April 12, 1807, Adams: Randolph, 216-17.)
[1029] Hildreth, iv, 692.
[1030] Parton: Burr, 458.
[1031] Parton: Jackson, i, 333.
[1032] Jackson to Anderson, June 16, 1807, ib. 334.
[1033] Ib. 335.
[1034] Ib. 334-36.
[1035] Parton: Burr, 606-08; see also Parton: Jackson, ii, 258-
59, 351-54; and Davis, ii, 433-36.
[1036] Address of John Tyler, "Richmond and its Memories,"
Tyler, i, 219.
[1037] Parton: Burr, 459.
[1038] Memoirs of Lieut.-General Scott, i, 13.
[1039] Memoirs of Lieut.-General Scott, i, 13, 16.
[1040] See Great American Lawyers: Lewis, ii, 268-75.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-69-320.jpg)
![Kennedy says that the stories of Wirt's habits of intoxication
were often exaggerated (Kennedy, i, 68); but see his description
of the bar of that period and his apologetic reference to Wirt's
conviviality (ib. 66-67).
[1041] Blennerhassett Papers: Safford, 426.
[1042] Parton: Burr, 461.
[1043] Burr Trials, i, 31-32.
[1044] Ib. 37.
[1045] Ib. 38.
[1046] Meaning the partiality of the persons challenged, such
as animosity toward the accused, conduct showing bias against
him, and the like. See Bouvier's Law Dictionary: Rawle, 3d
revision, ii, 1191.
[1047] Burr Trials, i, 38-39.
[1048] Ib. 41-42.
[1049] Burr Trials, i, 41-42.
[1050] Jefferson to Nicholas, Feb. 28, 1807, Works: Ford, x,
370-71.
[1051] Burr Trials, i, 43.
[1052] Ib. 44.
[1053] In view of the hatred which Marshall knew Randolph felt
toward Jefferson, it is hard to reconcile his appointment with the
fairness which Marshall tried so hard to display throughout the
trial. However, several of Jefferson's most earnest personal
friends were on the grand jury, and some of them were very
powerful men. Also fourteen of the grand jury were Republicans
and only two were Federalists.
[1054] Burr Trials, i, 45-46. This grand jury included some of
the foremost citizens of Virginia. The sixteen men who composed
this body were: John Randolph, Jr., Joseph Eggleston, Joseph C.
Cabell, Littleton W. Tazewell, Robert Taylor, James Pleasants, John](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-70-320.jpg)
![Brockenbrough, William Daniel, James M. Garnett, John Mercer,
Edward Pegram, Munford Beverly, John Ambler, Thomas Harrison,
Alexander Shephard, and James Barbour.
[1055] Marshall's error in this opinion, or perhaps the
misunderstanding of a certain passage of it (see supra, 350),
caused him infinite perplexity during the trial; and he was put to
his utmost ingenuity to extricate himself. The misconstruction by
the grand jury of the true meaning of Marshall's charge was one
determining cause of the grand jury's decision to indict Burr. (See
infra, 466.)
[1056] Burr Trials, i, 47-48.
[1057] Hay to Jefferson, May 25, 1807, Jefferson MSS. Lib.
Cong.
[1058] Burr Trials, i, 48-51.
[1059] Burr Trials, i, 53-54.
[1060] Irving to Paulding, June 22, 1807, Life and Letters of
Washington Irving: Irving, i, 145.
[1061] Burr Trials, i, 57-58.
[1062] Burr Trials, i, 58-76.
[1063] "I ... contented myself ... with ... declaring to the
Audience (for two thirds of our speeches have been addressed to
the people) that I was prepared to give the most direct
contradiction to the injurious Statements." (Hay to Jefferson, June
14, 1807, giving the President an account of the trial, Jefferson
MSS. Lib. Cong.)
[1064] He was hanged in effigy soon after the trial. (See infra,
539.)
[1065] It must be remembered that Marshall himself declared,
in the very midst of the contest, that it would be dangerous for a
jury to acquit Burr. (See supra, 401.)
[1066] He had narrowly escaped impeachment (see supra,
chap. iv), and during the trial he was openly threatened with that
ordeal (see infra, 500).](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-71-320.jpg)
![[1067] Burr Trials, i, 79-81.
[1068] See supra, 390-91.
[1069] Jefferson to Hay, May 26, 1807, Works: Ford, x, footnote
to 394-95.
[1070] Burr Trials, i, 81-82.
[1071] Ib. 82.
[1072] Ib. 84-85.
[1073] Burr Trials, i, 91.
[1074] Ib. 94.
[1075] Ib. 95-96.
[1076] Burr Trials, i, 492-97.
[1077] Burr Trials, i, 509-14.
[1078] Burr Trials, i, 97-101.
[1079] Ib. 97.
[1080] Md. Hist. Soc. Fund-Pub. No. 24, 22.
[1081] Blennerhassett Papers: Safford, 468-69.
[1082] Burr Trials, i, 101-04.
[1083] Burr Trials, i, 105.
[1084] The men who went on this second bail bond for Burr
were: William Langburn, Thomas Taylor, John G. Gamble, and
Luther Martin. (Ib. 106.)
[1085] Blennerhassett Papers: Safford, 315-16.
[1086] Eaton: Prentiss, 396-403; 4 Cranch, 463-66.
[1087] Blennerhassett Papers: Safford, 425.
[1088] Jefferson to Hay, May 28, 1807, Works: Ford, x, 395-96.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-72-320.jpg)
![[1089] Jefferson to Eppes, May 28, 1807, Works: Ford, x, 412-
13.
[1090] Hay to Jefferson, May 31, 1807, Jefferson MSS. Lib.
Cong.
[1091] Jefferson to Hay, June 2, 1807, Works: Ford, x, 396-97.
[1092] Same to same, June 5, 1807, ib. 397-98; Hay to
Jefferson, same date, Jefferson MSS. Lib. Cong.; and others cited,
infra.
[1093] Jefferson to Dayton, Aug. 17, 1807, Works: Ford, x, 478.
[1094] Irving to Mrs. Hoffman, June 4, 1807, Irving, i, 142.
[1095] Ib.
[1096] Burr had seen the order in the Natchez Gazette. It was
widely published.
[1097] Burr Trials, i, 113-14.
[1098] Burr Trials, i, 115-18.
[1099] Hay to Jefferson, June 9, 1807, Jefferson MSS. Lib.
Cong.
[1100] Jefferson to Hay, June 12, 1807, Works: Ford, x, 398-99.
[1101] Burr Trials, i, 124-25.
[1102] Irving to Mrs. Hoffman, June 4, 1807, Irving, i, 143.
[1103] Martin here refers to what he branded as "the farcical
trials of Ogden and Smith." In June and July, 1806, William S.
Smith and Samuel G. Ogden of New York were tried in the United
States Court for that district upon indictments charging them with
having aided Miranda in his attack on Caracas, Venezuela. They
made affidavit that the testimony of James Madison, Secretary of
State, Henry Dearborn, Secretary of War, Robert Smith, Secretary
of the Navy, and three clerks of the State Department, was
necessary to their defense. Accordingly these officials were
summoned to appear in court. They refused, but on July 8, 1806,
wrote to the Judges—William Paterson of the Supreme Court and](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-73-320.jpg)
![Matthias B. Talmadge, District Judge—that the President "has
specially signified to us that our official duties cannot ... be at this
juncture dispensed with." (Trials of Smith and Ogden: Lloyd,
stenographer, 6-7.)
The motion for an attachment to bring the secretaries and their
clerks into court was argued for three days. The court disagreed,
and no action therefore was taken. (Ib. 7-90.) One judge
(undoubtedly Paterson) was "of opinion, that the absent
witnesses should be laid under a rule to show cause, why an
attachment should not be issued against them"; the other
(Talmadge) held "that neither an attachment in the first instance,
nor a rule to show cause ought to be granted." (Ib. 89.)
Talmadge was a Republican, appointed by Jefferson, and
charged heavily against the defendants (ib. 236-42, 287); but
they were acquitted.
The case was regarded as a political prosecution, and the
refusal of Cabinet officers and department clerks to obey the
summons of the court, together with Judge Talmadge's
disagreement with Justice Paterson—who in disgust immediately
left the bench under plea of ill-health (ib. 90)—and the
subsequent conduct of the trial judge, were commented upon
unfavorably. These facts led to Martin's reference during the Burr
trial.
[1104] Burr Trials, i, 127-28.
[1105] Burr Trials, i, 130-33.
[1106] Ib. 134-35.
[1107] Burr Trials, i, 137-45.
[1108] Burr Trials, i, 147-48.
[1109] Ib. 148-52.
[1110] Burr Trials, i, 153-64.
[1111] Burr Trials, i, 164-67.
[1112] Ib. 173-76.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-74-320.jpg)
![[1113] Burr Trials, i, 177.
[1114] See infra, 455-56.
[1115] Burr Trials, i, 181-83.
[1116] United States vs. Smith and Ogden. (See supra, 436,
foot-note.)
[1117] Burr Trials, i, 187-88.
[1118] Burr Trials, i, 189.
[1119] Hay to Jefferson, June 14, 1807, Jefferson MSS. Lib.
Cong.
[1120] Ambler: Thomas Ritchie—A Study in Virginia Politics, 40-
41.
[1121] Jefferson to Hay, June 17, 1807, Works: Ford, x, 400-01.
[1122] Jefferson to Hay, June 19, 1807, Works: Ford, x, 402-03.
[1123] Burr Trials, i, 190.
[1124] Burr Trials, i, 191-93.
[1125] Burr Trials, i, 193-96.
[1126] Jefferson to Hay, June 20, 1807, Works: Ford, x, 403-05.
[1127] Hay to Jefferson, June 11, 1807, Jefferson MSS. Lib.
Cong. This letter announced Wilkinson's landing at Hampton
Roads.
Wilkinson reached Richmond by stage on Saturday, June 13. He
was accompanied by John Graham and Captain Gaines, the
ordinary witnesses having been sent ahead on a pilot boat.
(Graham to Madison, May 11, 1807, "Letters in Relation," MSS.
Lib. Cong.) Graham incorrectly dated his letter May 11 instead of
June 11. He had left New Orleans in May, and in the excitement
of landing had evidently forgotten that a new month had come.
Wilkinson was "too much fatigued" to come into court. (Burr
Trials, i, 196.) By Monday, however, he was sufficiently restored to
present himself before Marshall.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-75-320.jpg)
![[1128] Irving to Paulding, June 22, 1807, Irving, i, 145.
[1129] Wilkinson to Jefferson, June 17, 1807, "Letters in
Relation," MSS. Lib. Cong.
The court reporter impartially states that Wilkinson was "calm,
dignified, and commanding," and that Burr glanced at him with
"haughty contempt." (Burr Trials, i, footnote to 197.)
[1130] "Gen: Jackson of Tennessee has been here ever since
the 22ḍ [of May] denouncing Wilkinson in the coarsest terms in
every company." (Hay to Jefferson, June 14, 1807, Jefferson MSS.
Lib. Cong.)
Hay had not the courage to tell the President that Jackson had
been as savagely unsparing in his attacks on Jefferson as in his
thoroughly justified condemnation of Wilkinson.
[1131] Truxtun left the Navy in 1802, and, at the time of the
Burr trial, was living on a farm in New Jersey. No officer in any
navy ever made a better record for gallantry, seamanship, and
whole-hearted devotion to his country. The list of his successful
engagements is amazing. He was as high-spirited as he was
fearless and honorable.
In 1802, when in command of the squadron that was being
equipped for our war with Tripoli, Truxtun most properly asked
that a captain be appointed to command the flagship. The Navy
was in great disfavor with Jefferson and the whole Republican
Party, and naval affairs were sadly mismanaged or neglected.
Truxtun's reasonable request was refused by the Administration,
and he wrote a letter of indignant protest to the Secretary of the
Navy. To the surprise and dismay of the experienced and
competent officer, Jefferson and his Cabinet construed his spirited
letter as a resignation from the service, and, against Truxtun's
wishes, accepted it as such. Thus the American Navy lost one of
its ablest officers at the very height of his powers. Truxtun at the
time was fifty-two years old. No single act of Jefferson's
Administration is more discreditable than this untimely ending of
a great career.
[1132] This man was the elder Decatur, father of the more
famous officer of the same name. He had had a career in the
American Navy as honorable but not so distinguished as that of](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-76-320.jpg)
![Truxtun; and his service had been ended by an unhappy
circumstance, but one less humiliating than that which severed
Truxtun's connection with the Navy.
The unworthiest act of the expiring Federalist Congress of
1801, and one which all Republicans eagerly supported, was that
authorizing most of the ships of the Navy to be sold or laid up
and most of the naval officers discharged. (Act of March 3, 1801,
Annals, 6th Cong. 1st and 2d Sess. 1557-59.) Among the men
whose life profession was thus cut off, and whose notable
services to their country were thus rewarded, was Commodore
Stephen Decatur, who thereafter engaged in business in
Philadelphia.
[1133] It was under Stoddert's administration of the Navy
Department that the American Navy was really created. Both
Truxtun and Decatur won their greatest sea battles in our naval
war with France, while Stoddert was Secretary. The three men
were close friends and all of them warmly resented the demolition
of the Navy and highly disapproved of Jefferson, both as an
individual and as a statesman. They belonged to the old school of
Federalists. Three more upright men did not live.
[1134] See supra, 304-05.
[1135] A popular designation of Eaton after his picturesque and
heroic Moroccan exploit.
[1136] Truxtun at the time of his conversations with Burr was
in the thick of that despair over his cruel and unjustifiable
separation from the Navy, which clouded his whole after life. The
longing to be once more on the quarter-deck of an American
warship never left his heart.
[1137] Burr Trials, i, 486-91. This abstract is from the
testimony given by Commodore Truxtun before the trial jury,
which was substantially the same as that before the grand jury.
[1138] Annals, 10th Cong. 1st Sess. 452-63. See note 1, next
page.
[1139] Wilkinson's testimony on the trial for misdemeanor
(Annals, 10th Cong. 1st Sess, 520-22) was the same as before
the grand jury.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-77-320.jpg)
!["Wilkinson is now before the grand jury, and has such a mighty
mass of words to deliver himself of, that he claims at least two
days more to discharge the wondrous cargo." (Irving to Paulding,
June 22, 1807, Irving, i, 145.)
[1140] See McCaleb, 335. Politics alone saved Wilkinson. The
trial was universally considered a party matter, Jefferson's
prestige, especially, being at stake. Yet seven out of the sixteen
members of the grand jury voted to indict Wilkinson. Fourteen of
the jury were Republicans, and two were Federalists.
[1141] Randolph to Nicholson, June 25, 1807, Adams:
Randolph, 221-22. Speaking of political conditions at that time,
Randolph observed: "Politics have usurped the place of law, and
the scenes of 1798 [referring to the Alien and Sedition laws] are
again revived."
[1142] Testimony of Joseph C. Cabell, one of the grand jury.
(Annals, 10th Cong. 1st Sess. 677.)
[1143] "Mr. Swartwout ... discovered the utmost frankness and
candor in his evidence.... The very frank and candid manner in
which he gave his testimony, I must confess, raised him very high
in my estimation, and induced me to form a very different opinion
of him from that which I had before entertained." (Testimony of
Littleton W. Tazewell, one of the grand jury, Annals, 10th Cong.
1st Sess. 633.)
"The manner of Mr. Swartwout was certainly that of conscious
innocence." (Testimony of Joseph C. Cabell, one of the grand jury,
ib. 677.)
[1144] See supra, 426-27.
[1145] Forty-eight witnesses were examined by the grand jury.
The names are given in Brady: Trial of Aaron Burr, 69-70.
[1146] Burr Trials, i, 305-06; also "Bills of Indictment," MSS.
Archives of the United States Court, Richmond, Va.
The following day former Senator Jonathan Dayton of New
Jersey, Senator John Smith of Ohio, Comfort Tyler and Israel
Smith of New York, and Davis Floyd of the Territory of Indiana,
were presented for treason. How Bollmann, Swartwout, Adair,
Brown, and others escaped indictment is only less](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-78-320.jpg)
![comprehensible than the presentment of Tyler, Floyd, and the two
Smiths for treason.
[1147] Blennerhassett Papers: Safford, 314. "Two of the most
respectable and influential of that body, since it has been
discharged, have declared they mistook the meaning of Chief
Justice Marshall's opinion as to what sort of acts amounted to
treason in this country, in the case of Swartwout and Ogden
[Bollmann]; that it was under the influence of this mistake they
concurred in finding such a bill against A. Burr, which otherwise
would have probably been ignored."
[1148] Burr Trials, i, 327-28.
[1149] Hay to Jefferson, June 25, 1807, Jefferson MSS. Lib.
Cong.
[1150] Burr Trials, i, 197-357.
[1151] This was one of Luther Martin's characteristic outbursts.
Every word of it, however, was true.
[1152] Burr Trials, i, 197-357.](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-79-320.jpg)
![CHAPTER IX
WHAT IS TREASON?
No person shall be convicted of Treason unless on the Testimony of two
Witnesses to the same overt Act, or on Confession in open Court. (Constitution,
Article III, Section 3.)
Such are the jealous provisions of our laws in favor of the accused that I
question if he can be convicted. (Jefferson.)
The scenes which have passed and those about to be transacted will hereafter
be deemed fables, unless attested by very high authority. (Aaron Burr.)
That this court dares not usurp power is most true. That this court dares not
shrink from its duty is no less true. (Marshall.)
While the grand jury had been examining witnesses, interesting
things had taken place in Richmond. Burr's friends increased in
number and devotion. Many of them accompanied him to and from
court each day.[1153] Dinners were given in his honor, and Burr
returned these courtesies, sometimes entertaining at his board a
score of men and women of the leading families of the city.[1154]
Fashionable Richmond was rapidly becoming Burr-partisan. In
society, as at the bar, the Government had been maneuvered into
defense. Throughout the country, indeed, Burr's numerous
adherents had proved stanchly loyal to him.
"I believe," notes Senator Plumer in his diary, "even at this period,
that no man in this country, has more personal friends or who are
more firmly attached to his interests—or would make greater
sacrifices to aid him than this man."[1155] But this availed Burr
nothing as against the opinion of the multitude, which Jefferson
manipulated as he chose. Indeed, save in Richmond, this very](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-80-320.jpg)
![fidelity of Burr's friends served rather to increase the public
animosity; for many of these friends were persons of standing, and
this fact did not appeal favorably to the rank and file of the rampant
democracy of the period.
In Richmond, however, Burr's presence and visible peril animated
his followers to aggressive action. On the streets, in the taverns and
drinking-places, his adherents grew bolder. Young Swartwout
chanced to meet the bulky, epauletted Wilkinson on the sidewalk.
Flying into "a paroxysm of disgust and rage," Burr's youthful
follower[1156] shouldered the burly general "into the middle of the
street." Wilkinson swallowed the insult. On learning of the incident
Jackson "was wild with delight."[1157] Burr's enemies were as furious
with anger. To spirited Virginians, only treason itself was worse than
the refusal of Wilkinson, thus insulted, to fight.
Swartwout, perhaps inspired by Jackson, later confirmed this
public impression of Wilkinson's cowardice. He challenged the
General to a duel; the hero refused—"he held no correspondence
with traitors or conspirators," he loftily observed;[1158] whereupon
the young "conspirator and traitor" denounced, in the public press,
the commander of the American armies as guilty of treachery,
perjury, forgery, and cowardice.[1159] The highest officer in the
American military establishment "posted for cowardice" by a mere
stripling! More than ever was Swartwout endeared to Jackson.
Soon after his arrival at Richmond, and a week before Burr was
indicted, Wilkinson perceived, to his dismay, the current of public
favor that was beginning to run toward Burr; and he wrote to
Jefferson in unctuous horror: "I had anticipated that a deluge of
Testimony would have been poured forth from all quarters, to
overwhelm Him [Burr] with guilt & dishonour—... To my
Astonishment I found the Traitor vindicated & myself condemned by
a Mass of Wealth Character-influence & Talents—merciful God what
a Spectacle did I behold—Integrity & Truth perverted & trampled](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-81-320.jpg)
![under foot by turpitude & Guilt, Patriotism appaled & Usurpation
triumphant."[1160]
Wilkinson was plainly weakening, and Jefferson hastened to
comfort his chief witness: "No one is more sensible than myself of
the injustice which has been aimed at you. Accept I pray, my
salutations and assurances of respect and esteem."[1161]
Before the grand jury had indicted Burr and Blennerhassett,
Wilkinson suffered another humiliation. On the very day that the
General sent his wailing cry of outraged virtue to the President, Burr
gave notice that he would move that an attachment should issue
against Jefferson's hero for "contempt in obstructing the
administration of justice" by rifling the mails, imprisoning witnesses,
and extorting testimony by torture.[1162] The following day was
consumed in argument upon the motion that did not rise far above
bickering. Marshall ruled that witnesses should be heard in support
of Burr's application, and that Wilkinson ought to be present.[1163]
Accordingly, the General was ordered to come into court.
James Knox, one of the young men who had accompanied Burr on
his disastrous expedition, had been brought from New Orleans as a
witness for the Government. He told a straightforward story of
brutality inflicted upon him because he could not readily answer the
printed questions sent out by Jefferson's Attorney-General.[1164] By
other witnesses it appeared that letters had been improperly taken
from the post-office in New Orleans.[1165] An argument followed in
which counsel on both sides distinguished themselves by the
learning and eloquence they displayed.[1166]
It was while Botts was speaking on this motion to attach
Wilkinson, that the grand jury returned the bills of indictment.[1167]
So came the dramatic climax.
Instantly the argument over the attachment of Wilkinson was
suspended. Burr said that he would "prove that the indictment](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-82-320.jpg)
![against him had been obtained by perjury"; and that this was a
reason for the court to exercise its discretion in his favor and to
accept bail instead of imprisoning him.[1168] Marshall asked Martin
whether he had "any precedent, where a court has bailed for
treason, after the finding of a grand jury," when "the testimony ...
had been impeached for perjury," or new testimony had been
presented to the court.[1169] For once in his life, Martin could not
answer immediately and offhand. So that night Aaron Burr slept in
the common jail at Richmond.
"The cup of bitterness has been administered to him with
unsparing hand," wrote Washington Irving.[1170] But he did not
quail. He was released next morning upon a writ of habeas corpus;
[1171] the argument on the request for the attachment of Wilkinson
was resumed, and for three days counsel attacked and counter-
attacked.[1172] On June 26, Burr's attorneys made oath that
confinement in the city jail was endangering his health; also that
they could not, under such conditions, properly consult with him
about the conduct of his case. Accordingly, Marshall ordered Burr
removed to the house occupied by Luther Martin; and to be confined
to the front room, with the window shutters secured by bars, the
door by a padlock, and the building guarded by seven men. Burr
pleaded not guilty to the indictments against him, and orders were
given for summoning the jury to try him.[1173]
Finally, Marshall delivered his written opinion upon the motion to
attach Wilkinson. It was unimportant, and held that Wilkinson had
not been shown to have influenced the judge who ordered Knox
imprisoned or to have violated the laws intentionally. The Chief
Justice ordered the marshal to summon, in addition to the general
panel, forty-eight men to appear on August 3 from Wood County, in
which Blennerhassett's island was located, and where the indictment
charged that the crime had been committed.[1174]](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-83-320.jpg)
![Five days before Marshall adjourned court in order that jurymen
might be summoned and both prosecution and defense enabled to
prepare for trial, an event occurred which proved, as nothing else
could have done, how intent were the people on the prosecution of
Burr, how unshakable the tenacity with which Jefferson pursued him.
On June 22, 1807, the British warship, the Leopard, halted the
American frigate, the Chesapeake, as the latter was putting out to
sea from Norfolk. The British officers demanded of Commodore
James Barron to search the American ship for British deserters and
to take them if found. Barron refused. Thereupon the Leopard,
having drawn alongside the American vessel, without warning
poured broadsides into her until her masts were shot away, her
rigging destroyed, three sailors killed and eighteen wounded. The
Chesapeake had not been fitted out, was unable to reply, and finally
was forced to strike her colors. The British officers then came on
board and seized the men they claimed as deserters, all but one of
whom were American-born citizens.[1175]
The whole country, except New England, roared with anger when
the news reached the widely separated sections of it; but the
tempest soon spent its fury. Quickly the popular clamor returned to
the "traitor" awaiting trial at Richmond. Nor did this "enormity," as
Jefferson called the attack on the Chesapeake,[1176] committed by a
foreign power in American waters, weaken for a moment the
President's determination to punish the native disturber of our
domestic felicity.
The news of the Chesapeake outrage arrived at Richmond on June
25, and John Randolph supposed that, of course, Jefferson would
immediately call Congress in special session.[1177] The President did
nothing of the kind. Wilkinson, as Commander of the Army, advised
him against armed retaliation. The "late outrage by the British,"
wrote the General, "has produced ... a degree of Emotion bordering
on rage—I revere the Honourable impulse but fear its Effects—...
The present is no moment for precipitancy or a stretch of power—on](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-84-320.jpg)
![the contrary the British being prepared for War & we not, a sudden
appeal to hostilities will give them a great advantage—... The efforts
made here [Richmond] by a band of depraved Citizens, in
conjunction with an audacious phalanx of insolent exotics, to save
Burr, will have an ultimate good Effect, for the national Character of
the Ancient dominion is in display, and the honest impulses of true
patriotism will soon silence the advocates of usurpation without &
conspiracy within."
Wilkinson tells Jefferson that he is coming to Washington forthwith
to pay his "respects," and concludes: "You are doubtless well
advised of proceedings here in the case of Burr—to me they are
incomprehensible as I am no Jurist—The Grand Jury actually made
an attempt to present me for Misprision of Treason—... I feel myself
between 'Scylla and Carybdis' the Jury would Dishonor me for failing
of my Duty, and Burr & his Conspirators for performing it—"[1178]
Not until five weeks after the Chesapeake affair did the President
call Congress to convene in special session on October 26—more
than four months after the occurrence of the crisis it was summoned
to consider.[1179] But in the meantime Jefferson had sent a
messenger to advise the American Minister in London to tell the
British Government what had happened, and to demand a disavowal
and an apology.
Meanwhile, the Administration vigorously pushed the prosecution
of the imprisoned "traitor" at Richmond.[1180] Hay was dissatisfied
that Burr should remain in Martin's house, even under guard and
with windows barred and door locked; and he obtained from the
Executive Council of Virginia a tender to the court of "apartments on
the third floor" of the State Penitentiary for the incarceration of the
prisoner. Burr's counsel strenuously objected, but Marshall ordered
that he be confined there until August 2, at which time he should be
returned to the barred and padlocked room in Martin's house.[1181]](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-85-320.jpg)
![In the penitentiary, "situated in a solitary place among the hills" a
mile and a half from Richmond,[1182] Burr remained for five weeks.
Three large rooms were given him in the third story; the jailer was
considerate and kind; his friends called on him every day;[1183] and
servants constantly "arrived with messages, notes, and inquiries,
bringing oranges, lemons, pineapples, raspberries, apricots, cream,
butter, ice and some ordinary articles."[1184]
Burr wrote Theodosia of his many visitors, women as well as men:
"It is well that I have an ante-chamber, or I should often be gêné
with visitors." If Theodosia should come on for the trial, he playfully
admonishes her that there must be "no agitations, no complaints, no
fears or anxieties on the road, or I renounce thee."[1185]
Finally Burr asked his daughter to come to him: "I want an
independent and discerning witness to my conduct and that of the
government. The scenes which have passed and those about to be
transacted will exceed all reasonable credibility, and will hereafter be
deemed fables, unless attested by very high authority.... I should
never invite any one, much less those so dear to me, to witness my
disgrace. I may be immured in dungeons, chained, murdered in legal
form, but I cannot be humiliated or disgraced. If absent, you will
suffer great solicitude. In my presence you will feel none, whatever
be the malice or the power of my enemies, and in both they
abound."[1186]
Theodosia was soon with her father. Her husband, Joseph Alston,
now Governor of South Carolina, accompanied her; and she brought
her little son, who, almost as much as his beautiful mother, was the
delight of Burr's heart.
During these torrid weeks the public temper throughout the
country rose with the thermometer.[1187] The popular distrust of
Marshall grew into open hostility. A report of the proceedings, down
to the time when Burr was indicted for treason, was published in a
thick pamphlet and sold all over Virginia and neighboring States. The](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-86-320.jpg)
![impression which the people thus acquired was that Marshall was
protecting Burr; for had he not refused to imprison him until the
grand jury indicted the "traitor"?
The Chief Justice estimated the situation accurately. He knew,
moreover, that prosecutions for treason might be instituted
thereafter in other parts of the country, particularly in New England.
The Federalist leaders in that section had already spoken and written
sentiments as disloyal, essentially, as those now attributed to Burr;
and, at that very time, when the outcry against Burr was loudest,
they were beginning to revive their project of seceding from the
Union.[1188] To so excellent a politician and so far-seeing a
statesman as Marshall, it must have seemed probable that his party
friends in New England might be brought before the courts to
answer to the same charge as that against Aaron Burr.
At all events, he took, at this time, a wise and characteristically
prudent step. Four days after the news of the Chesapeake affair
reached Richmond, the Chief Justice asked his associates on the
Supreme Bench for their opinion on the law of treason as presented
in the case of Aaron Burr. "I am aware," he wrote, "of the
unwillingness with which a judge will commit himself by an opinion
on a case not before him, and on which he has heard no argument.
Could this case be readily carried before the Supreme Court, I would
not ask an opinion in its present stage. But these questions must be
decided by the judges separately on their respective circuits, and I
am sure that there would be a strong and general repugnance to
giving contradictory decisions on the same points. Such a
circumstance would be disreputable to the judges themselves as well
as to our judicial system. This suggestion suggests the propriety of a
consultation on new and different subjects and will, I trust, apologize
for this letter."[1189]
Whether a consultation was held during the five weeks that the
Burr trial was suspended is not known. But if the members of the
Supreme Court did not meet the Chief Justice, it would appear to be](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-87-320.jpg)
![certain that they wrote him their views of the American law of
treason; and that, in the crucial opinion which Marshall delivered on
that subject more than two months after he had written to his
associates, he stated their mature judgments as well as his own.
It was, therefore, with a composure, unwonted even for him, that
Marshall again opened court on August 3, 1807. The crowd was, if
possible, greater than ever. Burr entered the hall with his son-in-law,
Governor Alston.[1190] Not until a week later was counsel for the
Government ready to proceed. When at last the men summoned to
serve on the petit jury were examined as to their qualifications, it
was all but impossible to find one impartial man among them—
utterly impossible to secure one who had not formed opinions from
what, for months, had been printed in the newspapers.
Marshall described with fairness the indispensable qualifications of
a juror.[1191] Men were rejected as fast as they were questioned—all
had read the stories and editorial opinions that had filled the press,
and had accepted the deliberate judgment of Jefferson and the
editors; also, they had been impressed by the public clamor thus
created, and believed Burr guilty of treason. Out of forty-eight men
examined during the first day, only four could be accepted.[1192]
While the examination of jurors was in progress, one of the most
brilliant debates of the entire trial sprang up, as to the nature and
extent of opinions formed which would exclude a man from serving
on a jury.[1193]
When Marshall was ready to deliver his opinion, he had heard all
the reasoning that great lawyers could give on the subject, and had
listened to acute analyses of all the authorities. His statement of the
law was the ablest opinion he had yet delivered during the
proceedings, and is an admirable example of his best logical method.
It appears, however, to have been unnecessary, and was doubtless
delivered as a part of Marshall's carefully considered plan to go to](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-88-320.jpg)
![the extreme throughout the trial in the hearing and examination of
every subject.[1194]
For nearly two weeks the efforts to select a jury continued. Not
until August 15 were twelve men secured, and most of these
avowed that they had formed opinions that Burr was a traitor. They
were accepted only because impartial men could not be found.
When Marshall finished the reading of his opinion, Hay promptly
advised Jefferson that "the [bi]as of Judge Marshall is as obvious, as
if it was [stam]ped upon his forehead.... [He is] endeavoring to work
himself up to a state of [f]eeling which will enable [him] to aid Burr
throughout the trial, without appearing to be conscious of doing
wrong. He [Marshall] seems to think that his reputation is
irretrievably gone, and that he has now nothing to lose by doing as
he pleases.—His concern for Burr is wonderful. He told me many
years ago, when Burr was rising in the estimation of the republican
party, that he was as profligate in principle, as he was desperate in
fortune. I remember his words. They astonished me.
"Yet," complained Hay, "when the Gr: Jury brought in their bill the
Chief Justice gazed at him, for a long time, without appearing
conscious that he was doing so, with an expression of sympathy &
sorrow as strong, as the human countenance can exhibit without
palpable emotion. If Mr. Burr has any feeling left, yesterday must
have been a day of agonizing humiliation," because the answers of
the jurors had been uniformly against him; and Hay gleefully relates
specimens of them.
"There is but one chance for the accused," he continued, "and
that is a good one because it rests with the Chief Justice. It is
already hinted, but not by himself [that] the decision of the Supreme
Court will no[t be] deemed binding. If the assembly of men on
[Blennerhassett's is]land, can be pronounced 'not an overt act' [it
will] be so pronounced."[1195]](https://image.slidesharecdn.com/3375109-250530154159-8472565d/85/Advanced-Signal-Processing-Handbook-Theory-And-Implementation-For-Radar-Sonar-And-Medical-Imaging-Real-Time-Systems-Stergiopoulos-89-320.jpg)
Advanced Signal Processing Handbook Theory And Implementation For Radar Sonar And Medical Imaging Real Time Systems Stergiopoulos
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- 5. C R C R E V I V A L S C R C R E V I V A L S Advanced Signal Processing Handbook Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems Edited by Stergios Stergiopoulos ISBN 978-1-138-10482-2 ,!7IB1D8-baeicc! www.crcpress.com Advanced Signal Processing Handbook Edited by Stergios Stergiopoulos
- 6. ADVANCED SIGNAL PROCESSING HANDBOOK Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems
- 7. THE ELECTRICAL ENGINEERING AND SIGNAL PROCESSING SERIES Edited by Alexander Poularikas and Richard C. Dorf The Advanced Signal Processing Handbook: Theory and Implementationfor Radar, Sonar, and Medical Imaging Real-Time Systems Stergios Stergiopoulos The Transform and Data Compression Handbook K.R. Rao and P.C. Yip Forthcoming Titles Handbook ofAntennas in Wireless Communications Lai Chand Godara Propagation Data Handbookfor Wireless Communications Robert Crane The Digital Color Imaging Handbook Guarav Sharma Handbook of Neural Network Signal Processing Yu Hen Hu and Jeng-Neng Hwang Handbook of Multisensor Data Fusion David Hall Applications in Time Frequency Signal Processing Antonia Papandreou-Suppappola Noise Reduction in Speech Applications Gillian Davis Signal Processing in Noise Vyacheslav Tuzlukov Electromagnetic Radiation and the Human Body: Effects, Diagnosis and Therapeutic Technologies Nikolaos Uzunoglu and Konstantina S. Nikita
- 8. ADVANCED SIGNAL PROCESSING HANDBOOK Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems Edited by STERGIOS STERGIOPOULOS
- 9. First published 2001 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 Reissued 2018 by CRC Press © 2001 by Taylor & Francis CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organiza-tion that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. A Library of Congress record exists under LC control number: 00045432 Publisher’s Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent. Disclaimer The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact. ISBN 13: 978-1-138-10482-2 (hbk) ISBN 13: 978-1-315-14979-0 (ebk) Visit the Taylor & Lrancis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
- 10. Preface Recent advances in digital signal processing algorithms and computer technology have combined to provide the ability to produce real-time systems that have capabilities far exceeding those of a few years ago. The writing of this handbook was prompted by a desire to bring together some of the recent theoretical developments on advanced signal processing, and to provide a glimpse of how modern technology can be applied to the development of current and next-generation active and passive real time systems. The handbook is intended to serve as an introduction to the principles and applications of advanced signal processing. It will focus on the development of a generic processing structure that exploits the great degree of processing concept similarities existing among the radar, sonar, and medical imaging systems. A high-level view of the above real-time systems consists of a high-speed Signal Processor to provide mainstream signal processing for detection and initial parameter estimation, a Data Manager which supports the data and information processing functionality of the system, and a Display Sub- System through which the system operator can interact with the data structures in the data manager to make the most effective use of the resources at his command. The Signal Processor normally incorporates a few fundamental operations. For example, the sonar and radar signal processors include beamforming, “matched” filtering, data normalization, and image pro cessing. The first two processes are used to improve both the signal-to-noise ratio (SNR) and parameter estimation capability through spatial and temporal processing techniques. Data normalization is required to map the resulting data into the dynamic range of the display devices in a manner which provides a CFAR (constant false alarm rate) capability across the analysis cells. The processing algorithms for spatial and temporal spectral analysis in real-time systems are based on conventional FFT and vector dot product operations because they are computationally cheaper and more robust than the modern non-linear high resolution adaptive methods. However, these non-linear algorithms trade robustness for improved array gain performance. Thus, the challenge is to develop a concept which allows an appropriate mixture of these algorithms to be implemented in practical real-time systems. The non-linear processing schemes are adaptive and synthetic aperture beamformers that have been shown experimentally to provide improvements in array gain for signals embedded in partially correlated noise fields. Using system image outputs, target tracking, and localization results as performance criteria, the impact and merits of these techniques are contrasted with those obtained using the conventional processing schemes. The reported real data results show that the advanced processing schemes provide improvements in array gain for signals embedded in anisotropic noise fields. However, the same set of results demonstrates that these processing schemes are not adequate enough to be considered as a replacement for conventional processing. This restriction adds an additional element in our generic signal processing structure, in that the conventional and the advanced signal processing schemes should run in parallel in a real-time system in order to achieve optimum use of the advanced signal processing schemes of this study. v
- 11. The handbook also includes a generic concept for implementing successfully adaptive schemes with near-instantaneous convergence in 2-dimensional (2-D) and 3-dimensional (3-D) arrays of sensors, such as planar, circular, cylindrical, and spherical arrays. It will be shown that the basic step is to minimize the number of degrees of freedom associated with the adaptation process. This step will minimize the adaptive schemes convergence period and achieve near-instantaneous convergence for integrated active and passive sonar applications. The reported results are part of a major research project, which includes the definition of a generic signal processing structure that allows the implementation of adaptive and synthetic aperture signal processing schemes in real-time radar, sonar, and medical tomography (CT, MRI, ultrasound) systems that have 2-D and 3-D arrays of sensors. The material in the handbook will bridge a number of related fields: detection and estimation theory; filter theory (Finite Impulse Response Filters); 1-D, 2-D, and 3-D sensor array processing that includes conventional, adaptive, synthetic aperture beamforming and imaging; spatial and temporal spectral analysis; and data normalization. Emphasis will be placed on topics that have been found to be particularly useful in practice. These are several interrelated topics of interest such as the influence of medium on array gain system performance, detection and estimation theory, filter theory, space-time processing, conventional, adaptive processing, and model-based signal processing concepts. Moveover, the system concept similarities between sonar and ultrasound problems are identified in order to exploit the use of advanced sonar and model-based signal processing concepts in ultrasound systems. Furthermore, issues of information post-processing functionality supported by the Data Manager and the Display units of real-time systems of interest are addressed in the relevant chapters that discuss nor- malizers, target tracking, target motion analysis, image post-processing, and volume visualization methods. The presentation of the subject matter has been influenced by the authors’ practical experiences, and it is hoped that the volume will be useful to scientists and system engineers as a textbook for a graduate course on sonar, radar, and medical imaging digital signal processing. In particular, a number of chapters summarize the state-of-the-art application of advanced processing concepts in sonar, radar, and medical imaging X-ray CT scanners, magnetic resonance imaging, and 2-D and 3-D ultrasound systems. The focus of these chapters is to point out their applicability, benefits, and potential in the sonar, radar, and medical environments. Although an all-encompassing general approach to a subject is mathematically elegant, practical insight and understanding may be sacrificed. To avoid this problem and to keep the handbook to a reasonable size, only a modest introduction is provided. In consequence, the reader is expected to be familiar with the basics of linear and sampled systems and the principles of probability theory. Furthermore, since modern real-time systems entail sampled signals that are digitized at the sensor level, our signals are assumed to be discrete in time and the subsystems that perform the processing are assumed to be digital. It has been a pleasure for me to edit this book and to have the relevant technical exchanges with so many experts on advanced signal processing. I take this opportunity to thank all authors for their responses to my invitation to contribute. I am also greatful to CRC Press LLC and in particular to Bob Stern, Helena Redshaw, Naomi Lynch, and the staff in the production department for their truly professional cooperation. Finally, the support by the European Commission is acknowledged for awarding Professor Uzunoglu and myself the Fourier Euroworkshop Grant (HPCF-1999-00034) to organize two workshops that enabled the contributing authors to refine and coherently integrate the material of their chapters as a handbook on advanced signal processing for sonar, radar, and medical imaging system applications. Stergios Stergiopoulos vi
- 12. Editor Stergios Stergiopoulos received a B.Sc. degree from the University of Athens in 1976 and the M.S. and Ph.D. degrees in geophysics in 1977 and 1982, respectively, from York University, Toronto, Canada. Presently he is an Adjunct Professor at the Department of Electrical and Computer Engineering of the University of Western Ontario and a Senior Defence Scientist at Defence and Civil Institute of Environ mental Medicine (DCIEM) of the Canadian DND. Prior to this assignment and from 1988 and 1991, he was with the SACLANT Centre in La Spezia, Italy, where he performed both theoretical and experimental research in sonar signal processing. At SACLANTCEN, he developed jointly with Dr. Sullivan from NUWC an acoustic synthetic aperture technique that has been patented by the U.S. Navy and the Hellenic Navy. From 1984 to 1988 he developed an underwater fixed array surveillance system for the Hellenic Navy in Greece and there he was appointed senior advisor to the Greek Minister of Defence. From 1982 to 1984 he worked as a research associate at York University and in collaboration with the U.S. Army Ballistic Research Lab (BRL), Aberdeen, MD, on projects related to the stability of liquid-filled spin stabilized projectiles. In 1984 he was awarded a U.S. NRC Research Fellowship for BRL. He was Associate Editor for the IEEE Journal o f Oceanic Engineering and has prepared two special issues on Acoustic Synthetic Aperture and Sonar System Technology. His present interests are associated with the imple mentation of non-conventional processing schemes in multi-dimensional arrays of sensors for sonar and medical tomography (CT, MRI, ultrasound) systems. His research activities are supported by Canadian- DND Grants, by Research and Strategic Grants (NSERC-CANADA) ($300K), and by a NATO Collabo rative Research Grant. Recently he has been awarded with European Commission-ESPRIT/IST Grants as technical manager of two projects entitled “New Roentgen” and “MITTUG.” Dr. Stergiopoulos is a Fellow of the Acoustical Society of America and a senior member of the IEEE. He has been a consultant to a number of companies, including Atlas Elektronik in Germany, Hellenic Arms Industry, and Hellenic Aerospace Industry. vii
- 14. Contributors Dimos Baltas Department of Medical Physics and Engineering Strahlenklinik, Stadtische Kliniken Offenbach Offenbach, Germany Institute of Communication and Computer Systems National Technical University of Athens Athens, Greece Klaus Becker FGAN Research Institute for Communication, Information Processing, and Ergonomics (FKIE) Wachtberg, Germany James V. Candy Lawrence Livermore National Laboratory University of California Livermore, California, U.S.A. G. Clifford Carter Naval Undersea Warfare Center Newport, Rhode Island, U.S.A. N. Ross Chapman School of Earth and Ocean Sciences University of Victoria Victoria, British Columbia, Canada Ian Cunningham The John P. Robarts Research Institute University of Western Ontario London, Ontario, Canada Konstantinos K. Delibasis Institute of Communication and Computer Systems National Technical University of Athens Athens, Greece Amar Dhanantwari Defence and Civil Institute of Environmental Medicine Toronto, Ontario, Canada Reza M. Dizaji School of Earth and Ocean Sciences University of Victoria Victoria, British Columbia, Canada Donal B. Downey The John P. Robarts Research Institute University of Western Ontario London, Ontario, Canada Geoffrey Edelson Advanced Systems and Technology Sanders, A Lockheed Martin Company Nashua, New Hampshire, U.S.A. Aaron Fenster The John P. Robarts Research Institute University of Western Ontario London, Ontario, Canada Dimitris Hatzinakos Department of Electrical and Computer Engineering University of Toronto Toronto, Ontario, Canada Simon Haykin Communications Research Laboratory McMaster University Hamilton, Ontario, Canada Grigorios Karangelis Department of Cognitive Computing and Medical Imaging Fraunhofer Institute for Computer Graphics Darmstadt, Germany R. Lynn Kirlin School of Earth and Ocean Sciences University of Victoria Victoria, British Columbia, Canada Wolfgang Koch FGAN Research Institute for Communciation, Information Processing, and Ergonomics (FKIE) Wachtberg, Germany Christos Kolotas Department of Medical Physics and Engineering Strahlenklinik, Stadtische Kliniken Offenbach Offenbach, Germany Harry E. Martz, Jr. Lawrence Livermore National Laboratory University of California Livermore, California, U.S.A. ix
- 15. George K. Matsopoulos Institute of Communication and Computer Systems National Technical University of Athens Athens, Greece Charles A. McKenzie Cardiovascular Division Beth Israel Deaconess Medical Center and Harvard Medical School Boston, Massachusetts, U.S.A. Bernard E. McTaggart Naval Undersea Warfare Center (retired) Newport, Rhode Island, U.S.A. Sanjay K. Mehta Naval Undersea Warfare Center Newport, Rhode Island, U.S.A. Natasa Milickovic Department of Medical Physics and Engineering Strahlenklinik, Stadtische Kliniken Offenbach Offenbach, Germany Gerald R. Moran Lawson Research Institute and Department of Medical Biophysics University of Western Ontario London, Ontario, Canada Nikolaos A. Mouravliansky Institute of Communication and Computer Systems National Technical University of Athens Athens, Greece Arnulf Oppelt Siemens Medical Engineering Group Erlangen, Germany Kostantinos N. Plataniotis Department of Electrical and Computer Engineering University of Toronto Toronto, Ontario, Canada Andreas Pommert Institute of Mathematics and Computer Science in Medicine University Hospital Eppendorf Hamburg, Germany Frank S. Prato Lawson Research Institute and Department of Medical Biophysics University of Western Ontario London, Ontario, Canada John M. Reid Department of Biomedical Engineering Drexel University Philadelphia, Pennsylvania, U.S.A. Department of Radiology Thomas Jefferson University Philadelphia, Pennsylvania, U.S.A. Department of Bioengineering University of Washington Seattle, Washington, U.S.A. Georgios Sakas Department of Cognitive Computing and Medical Imaging Fraunhofer Institute for Computer Graphics Darmstadt, Germany Daniel J. Schneberk Lawrence Livermore National Laboratory University of California Livermore, California, U.S.A. Stergios Stergiopoulos Defence and Civil Institute of Environmental Medicine Toronto, Ontario, Canada Department of Electrical and Computer Engineering University of Western Ontario London, Ontario, Canada Edmund J. Sullivan Naval Undersea Warfare Center Newport, Rhode Island, U.S.A. Rebecca E. Thornhill Lawson Research Institute and Department of Medical Biophysics University of Western Ontario London, Ontario, Canada Nikolaos Uzunoglu Department of Electrical and Computer Engineering National Technical University of Athens Athens, Greece Nikolaos Zamboglou Department of Medical Physics and Engineering Strahlenklinik, Stadtische Kliniken Offenbach Offenbach, Germany Institute of Communication and Computer Systems National Technical University of Athens Athens, Greece x
- 16. Dedication To my lifelong companion Vicky, my son Steve, and my daughter Erene xi
- 18. Contents 1 Signal Processing Concept Similarities among Sonar, Radar, and Medical Imaging Systems Stergios Stergiopoulos 1.1 Introduction................................................................................................................................................ 1-1 1.2 Overview of a Real-Time System..........................................................................................................1-1 1.3 Signal Processor...........................................................................................................................................1-3 1.4 Data Manager and Display Sub-System...............................................................................................1-8 SECTION I General Topics on Signal Processing 2 Adaptive Systems for Signal Process Simon Haykin 2.1 The Filtering Problem................................................................................................................................2-1 2.2 Adaptive Filters.......................................................................................................................................... 2-2 2.3 Linear Filter Structures............................................................................................................................ 2-4 2.4 Approaches to the Development of Linear Adaptive Filtering Algorithms................................................................................................................2-8 2.5 Real and Complex Forms of Adaptive Filters..................................................................................2-13 2.6 Nonlinear Adaptive Systems: Neural Networks.............................................................................2-14 2.7 Applications...............................................................................................................................................2-24 2.8 Concluding Remarks..............................................................................................................................2-45 3 Gaussian Mixtures and Their Applications to Signal Processing Kostantinos N. Plataniotis and Dimitris Hatzinakos 3.1 Introduction..................................................................................................................................................3-2 3.2 Mathematical Aspects of Gaussian Mixtures.....................................................................................3-4 3.3 Methodologies for Mixture Parameter Estimation..........................................................................3-7 3.4 Computer Generation of Mixture Variables...................................................................................3-13 3.5 Mixture Applications..............................................................................................................................3-15 3.6 Concluding Remarks..............................................................................................................................3-32 4 Matched Field Processing — A Blind System Identification Technique N. Ross Chapman, Reza M. Dizaji, and R. Lynn Kirlin 4.1 Introduction................................................................................................................................................. 4-1 4.2 Blind System Identification.................................................................................................................... 4-2 4.3 Cross-Relation Matched Field Processor............................................................................................4-9 4.4 Time-Frequency Matched Field Processor...................................................................................... 4-14 xiii
- 19. 4.5 Higher Order Matched Field Processors.........................................................................................4-17 4.6 Simulation and Experimental Examples.......................................................................................... 4-22 5 Model-Based Ocean Acoustic Signal Processing JamesV . Candy and Edmund J. Sullivan 5.1 Introduction................................................................................................................................................5-2 5.2 Model-Based Processing......................................................................................................................... 5-5 5.3 State-Space Ocean Acoustic Forward Propagators.......................................................................5-16 5.4 Ocean Acoustic Model-Based Processing Applications...............................................................5-24 5.5 Summary............................................. 5-50 6 Advanced Beamformers Stergios Stergiopoulos 6.1 Introduction................................................................................................................................................6-3 6.2 Background................................................................................................................................................ 6-4 6.3 Theoretical Remarks................................................................................................................................6-7 6.4 Optimum Estimators for Array Signal Processing........................................................................6-14 6.5 Advanced Beamformers........................................................................................................................6-26 6.6 Implementation Considerations........................................................................................................6-37 6.7 Concept Demonstration: Simulations and Experimental Results............................................ 6-51 6.8 Conclusion...............................................................................................................................................6-66 7 Advanced Applications of Volume Visualization Methods in Medicine Georgios Sakas, Grigorios KarangeliSy and Andreas Pommert 7.1 Volume Visualization Principles.......................................................................................................... 7-2 7.2 Applications to Medical Data..............................................................................................................7-18 Appendix Principles of Image Processing: Pixel Brightness Transformations, Image Filtering and Image Restoration.............................................................................. 7-55 8 Target Tracking Wolfgang Koch 8.1 Introduction...................................................................................... 8-3 8.2 Discussion of the Problem......................................................................................................................8-6 8.3 Statistical Models......................................................................................................................................8-7 8.4 Bayesian Track Maintenance...............................................................................................................8-14 8.5 Suboptimal Realization.........................................................................................................................8-19 8.6 Selected Applications.............................................................................................................................8-27 9 Target Motion Analysis (TMA) Klaus Becker 9.1 Introduction................................................................................................................................................9-3 9.2 Features of the TMA Problem...............................................................................................................9-4 9.3 Solution of the TMA Problem...............................................................................................................9-9 9.4 Conclusion...............................................................................................................................................9-19 xiv
- 20. SECTION II Sonar and Radar System Applications 1 0 Sonar Systems G. Clifford Carter, Sanjay K. Mehta, and Bernard E. McTaggart 10.1 Introduction............................................................................................................................................. 10-2 10.2 Underwater Propagation...................................................................................................................... 10-4 10.3 Underwater Sound Systems: Components and Processes...........................................................10-8 10.4 Signal Processing Functions.............................................................................................................. 10-17 10.3 Advanced Signal Processing.............................................................................................................10-20 10.6 Application............................................................................................................................................10-22 1 1 Theory and Implementation of Advanced Signal Processing for Active and Passive Sonar Systems Stergios Stergiopoulos and Geoffrey Edelson 11.1 Introduction..............................................................................................................................................11-2 11.2 Theoretical Remarks.............................................................................................................................11-5 11.3 Real Results from Experimental Sonar Systems......................................................................... 11-27 11.4 Conclusion............................................................................................................................................11-41 1 2 Phased Array Radars Nikolaos Uzunoglu 12.1 Introduction............................................................................................................................................. 12-1 12.2 Fundamental Theory of Phased Arrays............................................................................................12-2 12.3 Analysis and Design of Phased Arrays.............................................................................................. 12-9 12.4 Array Architectures.............................................................................................................................. 12-12 12.5 Conclusion............................................................................................................................................. 12-13 SECTION III Medical Imaging System Applications 1 3 Medical Ultrasonic Imaging Systems John M. Reid 13.1 Introduction..............................................................................................................................................13-2 13.2 System Fundamentals............................................................................................................................ 13-4 13.3 Tissue Properties’ Influence on System Design.............................................................................. 13-7 13.4 Imaging Systems.......................................................................................................................................13-8 13.5 Conclusion..............................................................................................................................................13-15 1 4 Basic Principles and Applications of 3-D Ultrasound Imaging Aaron Fenster and Donal B. Downey 14.1 Introduction..............................................................................................................................................14-1 14.2 Limitations of Ultrasonography Addressed by 3-D Imaging.....................................................14-2 14.3 Scanning Techniques for 3-D Ultrasonography.............................................................................14-3 14.4 Reconstruction of the 3-D Ultrasound Images............................................................................14-15 14.5 Sources of Distortion in 3-D Ultrasound Imaging.....................................................................14-17 xv
- 21. 14.6 Viewing of 3-D Ultrasound Images................................................................................................14-19 14.7 3-D Ultrasound System Performance.............................................................................................14-23 14.8 Use of 3-D Ultrasound in Brachytherapy.....................................................................................14-27 14.9 Trends and Future Developments....................................................................................................14-28 1 5 Industrial Computed Tomographic Imaging Harry E. Martz, Jr. and Daniel J. Schneberk 15.1 Introduction.............................................................................................................................................15-1 15.2 CT Theory and Fundamentals............................................................................................................15-7 15.3 Selected Applications...........................................................................................................................15-22 15.4 Summary................................................................................................................................................ 15-43 15.5 Future W ork...........................................................................................................................................15-43 1 6 Organ Motion Effects in Medical CT Imaging Applications Ian Cunningham, Stergios Stergiopoulos, and Amar Dhanantwari 16.1 Introduction.............................................................................................................................................16-1 16.2 Motion Artifacts in C T ......................................................................................................................... 16-6 16.3 Reducing Motion Artifacts..................................................................................................................16-6 16.4 Reducing Motion Artifacts by Signal Processing — A Synthetic Aperture Approach... 16-11 16.5 Conclusions............................................................................................................................................16-31 1 7 Magnetic Resonance Tomography — Imaging with a Nonlinear System ArnulfOppelt 17.1 Introduction.............................................................................................................................................17-1 17.2 Basic NMR Phenomena........................................................................................................................ 17-2 17.3 Relaxation................................................................................................................................................. 17-4 17.4 NMR Signal..............................................................................................................................................17-4 17.5 Signal-to-Noise Ratio.............................................................................................................................17-7 17.6 Image Generation and Reconstruction.............................................................................................17-8 17.7 Selective Excitation..............................................................................................................................17-13 17.8 Pulse Sequences.....................................................................................................................................17-15 17.9 Influence of M otion............................................................................................................................17-20 17.10 Correction of Motion During Image Series.................................................................................. 17-23 17.11 Imaging of Flow....................................................................................................................................17-24 17.12 MR Spectroscopy................................................................................................................................. 17-26 17.13 System Design Considerations and Conclusions........................................................................ 17-27 17.14 Conclusion.............................................................................................................................................17-28 1 8 Functional Imaging of Tissues by Kinetic Modeling of Contrast Agents in MRI Frank S. Prato, Charles A. McKenzie, Rebecca E. Thornhill, and Gerald R. Moran 18.1 Introduction.............................................................................................................................................18-1 18.2 Contrast Agent Kinetic Modeling......................................................................................................18-2 xvi
- 22. 18.3 Measurement of Contrast Agent Concentration............................................................................18-3 18.4 Application of T 1 Farm to Bolus Tracking.................................................................................... 18-11 18.5 Summary..................................................................................................................................................18-15 1 9 Medical Image Registration and Fusion Techniques: A Review George K. MatsopoulosyKonstantinos K. Delibasis, and Nikolaos A. Mouravliansky 19.1 Introduction..............................................................................................................................................19-1 19.2 Medical Image Registration.................................................................................................................. 19-2 19.3 Medical Image Fusion.......................................................................................................................... 19-18 19.4 Conclusions.............................................................................................................................................19-24 2 0 The Role of Imaging in Radiotherapy Treatment Planning Dimos BaltasyNatasa Milickovic, Christos Kolotas, and Nikolaos Zamboglou 20.1 Introduction............................................................................................................................................. 20-1 20.2 The Role of Imaging in the External Beam Treatment Planning..............................................20-2 20.3 Introduction to Imaging Based Brachytherapy............................................................................20-13 20.4 Conclusion..............................................................................................................................................20-22 Index..........................................................................................................................................................1-1 xvii
- 24. I General Topics on Signal Processing 2 Adaptive Systems for Signal Process Simon Haykin ............................................................ 2-1 The Filtering Problem • Adaptive Filters • Linear Filter Structures • Approaches to the Development of Linear Adaptive Filtering Algorithms •Real and Complex Forms of Adaptive Filters • Nonlinear Adaptive Systems: Neural Networks • Applications • Concluding Remarks • References 3 Gaussian Mixtures and Their Applications to Signal Processing Kostantinos N. Plataniotis and Dimitris Hatzinakos .................................................................. 3-1 Nomenclature • Abstract • Introduction • Mathematical Aspects of Gaussian Mixtures • Methodologies for Mixture Parameter Estimation • Computer Generation of Mixture Variables • Mixture Applications • Concluding Remarks • References 4 Matched Field Processing — A Blind System Identification Technique N. Ross Chapman, Reza M. Dizaji, and R. Lynn Kirlin ............................................................ 4-1 Introduction •Blind System Identification •Cross-Relation Matched Field Processor •Time- Frequency Matched Field Processor • Higher Order Matched Field Processors • Simulation and Experimental Examples • References 5 Model-Based Ocean Acoustic Signal Processing James V. Candy and Edmund J. Sullivan ...................................................................................................................... 5-1 Abstract • Introduction • Model-Based Processing • State-Space Ocean Acoustic Forward Propagators •Ocean Acoustic Model-Based Processing Applications •Summary •References 6 Advanced Beamformers Stergios Stergiopoulos .......................................................................6-1 Abbreviations and Symbols •Introduction •Background •Theoretical Remarks •Optimum Estimators for Array Signal Processing • Advanced Beamformers • Implementation Considerations • Concept Demonstration: Simulations and Experimental Results • Conclusion • References 7 Advanced Applications of Volume Visualization Methods in Medicine Georgios Sakasy Grigoris Karangelis, and Andreas P om m ert......................................................7-1 Abstract • Volume Visualization Principles • Applications to Medical Data • Acknowledgments • References Appendix ...............................................................................................................................................7-55 Principles of Image Processing: Pixel Brightness Transformations, Image Filtering, and Image Restoration • References 8 Target Tracking Wolfgang Koch ....................................................................................................8-1 Abbreviations • Frequently Used Symbols • Introduction • Discussion of the Problem • Statistical Models • Bayesian Track Maintenance • Suboptimal Realization • Selected Applications • References
- 25. Advanced Signal Processing Handbook 9 Target Motion Analysis (TMA) Klaus B ecker..........................................................................9-1 Abbreviations and Symbols •Introduction • Features of the TMA Problem •Solution of the TMA Problem • Conclusion • References
- 26. 1 Signal Processing Concept Similarities among Sonar, Radar, and Medical Imaging Systems Stergios Stergiopoulos l.i Introduction................................................................................... 1-1 Defence and Civil Institute 1.2 Overview of a Real-Time System.............................................1-1 O f Environmental Medicine j .3 signal Processor..............................................................................1-3 University of Western Ontario SiSnal Conditioning of Array Sensor Time Series •Tomography Imaging CT/X-Ray and MRI Systems •Sonar, Radar, and Ultrasound Systems •Active and Passive Systems 1.4 Data Manager and Display Sub-System.................................1-8 Post-Processing for Sonarand Radar Systems • Post-Processing for Medical Imaging Systems •Signal and Target Tracking and Target Motion Analysis •Engineering Databases •Multi- Sensor Data Fusion References................................................................................................1-19 1.1 Introduction Several review articles on sonar,1 ’3-5 radar,2,3 and medical imaging3,6-14 system technologies have provided a detailed description of the mainstream signal processing functions along with their associated imple mentation considerations. The attempt of this handbook is to extend the scope of these articles by introducing an implementation effort of non-mainstream processing schemes in real-time systems. To a large degree, work in the area of sonar and radar system technology has traditionally been funded either directly or indirectly by governments and military agencies in an attempt to improve the capability of anti-submarine warfare (ASW) sonar and radar systems. A secondary aim of this handbook is to promote, where possible, wider dissemination of this military-inspired research. 1.2 Overview of a Real-Time System In order to provide a context for the material contained in this handbook, it would seem appropriate to briefly review the basic requirements of a high-performance real-time system. Figure 1.1 shows one possible high-level view of a generic system.1 5It consists of an array of sensors and/or sources; a high-speed signal 0-8493-3691-0/01/$0.Q0+$.50 t * © 2001 by CRC Press LLC 1 " 1
- 27. 12 Advanced Signal Processing Handbook FIGURE 1.1 Overview of a generic real-time system. It consists of an array of transducers, a signal processor to provide mainstream signal processing for detection and initial parameter estimation; a data manager, which supports the data, information processing functionality, and data fusion; and a display subsystem through which the system operator can interact with the manager to make the most effective use of the information available at his command. processor to provide mainstream signal processing for detection and initial parameter estimation; a data manager, which supports the data and information processing functionality of the system; and a display subsystem through which the system operator can interact with the data structures in the data manager to make the most effective use of the resources at his command. In this handbook, we will be limiting our attention to the signal processor, the data manager, and display subsystem , which consist of the algorithms and the processing architectures required for their imple mentation. Arrays o f sources and sensors include devices of varying degrees of complexity that illuminate the medium of interest and sense the existence of signals of interest. These devices are arrays of transducers having cylindrical, spherical, planar, or linear geometric configurations, depending on the application of interest. Quantitative estimates of the various benefits that result from the deployment of arrays of transducers are obtained by the array gain term, which will be discussed in Chapters 6,10, and 11. Sensor array design concepts, however, are beyond the scope of this handbook and readers interested in trans ducers can refer to other publications on the topic.16-19 The signal processor is probably the single, most important component of a real-time system of interest for this handbook. In order to satisfy the basic requirements, the processor normally incorporates the following fundamental operations: • Multi-dimensional beamforming • Matched filtering • Temporal and spatial spectral analysis • Tomography image reconstruction processing • Multi-dimensional image processing The first three processes are used to improve both the signal-to-noise ratio (SNR) and parameter estimation capability through spatial and the temporal processing techniques. The next two operations are image reconstruction and processing schemes associated mainly with image processing applications. As indicated in Figure 1.1, the replacement of the existing signal processor with a new signal processor, which would include advanced processing schemes, could lead to improved performance functionality
- 28. Processing Concept Similarities among Sonar, Radar, and Medical Systems 1-3 of a real-time system of interest, while the associated development cost could be significantly lower than using other hardware (H/W) alternatives. In a sense, this statement highlights the future trends of state- of-the-art investigations on advanced real-time signal processing functionalities that are the subject of the handbook. Furthemore, post-processing of the information provided by the previous operations includes mainly the following: • Signal tracking and target motion analysis • Image post-processing and data fusion • Data normalization • OR-ing These operations form the functionality of the data manager of sonar and radar systems. However, identification of the processing concept similarities between sonar, radar, and medical imaging systems may be valuable in identifying the implementation of these operations in other medical imaging system applications. In particular, the operation of data normalization in sonar and radar systems is required to map the resulting data into the dynamic range of the display devices in a manner which provides a constant false alarm rate (CFAR) capability across the analysis cells. The same operation, however, is required in the display functionality of medical ultrasound imaging systems as well. In what follows, each sub-system, shown in Figure 1.1, is examined briefly by associating the evolution of its functionality and characteristics with the corresponding signal processing technolog ical developments. 1.3 Signal Processor The implementation of signal processing concepts in real-time systems is heavily dependent on the computing architecture characteristics, and, therefore, it is limited by the progress made in this field. While the mathematical foundations of the signal processing algorithms have been known for many years, it was the introduction of the microprocessor and high-speed multiplier-accumulator devices in the early 1970s which heralded the turning point in the development of digital systems. The first systems were primarily fixed-point machines with limited dynamic range and, hence, were constrained to use conventional beamforming and filtering techniques.1,4,15As floating-point central processing units (CPUs) and supporting memory devices were introduced in the mid to late 1970s, multi-processor digital systems and modern signal processing algorithms could be considered for implementation in real-time systems. This major breakthrough expanded in the 1980s into massively parallel architectures supporting multi sensor requirements. The limitations associated with these massively parallel architectures became evident by the fact that they allow only fast-Fourier-transform (FFT), vector-based processing schemes because of efficient imple mentation and of their very cost-effective throughput characteristics. Thus, non-conventional schemes (i.e., adaptive, synthetic aperture, and high-resolution processing) could not be implemented in these types of real-time systems of interest, even though their theoretical and experimental developments suggest that they have advantages over existing conventional processing approaches.2,3,15,20-25 It is widely believed that these advantages can address the requirements associated with the difficult operational problems that next generation real-time sonar, radar, and medical imaging systems will have to solve. New scalable computing architectures, however, which support both scalar and vector operations satisfying high input/output bandwidth requirements of large multi-sensor systems, are becoming avail able.1 5 Recent frequent announcements include successful developments of super-scalar and massively parallel signal processing computers that have throughput capabilities of hundred of billions of floating point operations per second (GFLOPS).3 1 This resulted in a resurgence of interest in algorithm develop ment of new covariance-based, high-resolution, adaptive15,20-22,25 and synthetic aperture beamforming algorithms,15,23 and time-frequency analysis techniques.2 4
- 29. 1-4 Advanced Signal Processing Handbook Chapters 2, 3, 6, and 11 discuss in some detail the recent developments in adaptive, high-resolution, and synthetic aperture array signal processing and their advantages for real-time system applications. In particular, Chapter 2 reviews the basic issues involved in the study of adaptive systems for signal pro cessing. The virtues of this approach to statistical signal processing may be summarized as follows: • The use of an adaptive filtering algorithm, which enables the system to adjust its free parameters (in a supervised or unsupervised manner) in accordance with the underlying statistics of the environment in which the system operates, hence, avoiding the need for determining the statistical characteristics of the environment • Tracking capability, which permits the system to follow statistical variations (i.e., non-stationarity) of the environment • The availability of many different adaptive filtering algorithms, both linear and non-linear, which can be used to deal with a wide variety of signal processing applications in radar, sonar, and biomedical imaging • Digital implementation of the adaptive filtering algorithms, which can be carried out in hardware or software form In many cases, however, special attention is required for non-linear, non-Gaussian signal processing applications. Chapter 3 addresses this topic by introducing a Gaussian mixture approach as a model in such problems where data can be viewed as arising from two or more populations mixed in varying proportions. Using the Gaussian mixture formulation, problems are treated from a global viewpoint that readily yields and unifies previous, seemingly unrelated results. Chapter 3 introduces novel signal pro cessing techniques applied in applications problems, such as target tracking in polar coordinates and interference rejection in impulsive channels. In other cases these advanced algorithms, introduced in Chapters 2 and 3, trade robustness for improved performance.15,25,26 Furthermore, the improvements achieved are generally not uniform across all signal and noise environments of operational scenarios. The challenge is to develop a concept which allows an appropriate mixture of these algorithms to be implemented in practical real-time systems. The advent of new adaptive processing techniques is only the first step in the utilization of a priori information as well as more detailed information for the mediums of the propagating signals of interest. O f particular interest is the rapidly growing field of matched field processing (MFP).26 The use of linear models will also be challenged by techniques that utilize higher order statistics,24 neural networks,27 fuzzy systems,28 chaos, and other non-linear approaches. Although these concerns have been discussed27in a special issue of the IEEE Journal o f Oceanic Engineering devoted to sonar system technology, it should be noted that a detailed examination of MFP can be found also in the July 1993 issue of this journal which has been devoted to detection and estimation of MFP.29 The discussion in Chapter 4 focuses on the class of problems for which there is some information about the signal propagation model. From the basic formalism of blind system identification process, signal processing methods are derived that can be used to determine the unknown parameters of the medium transfer function and to demonstrate its performance for estimating the source location and the environmental parameters of a shallow water waveguide. Moreover, the system concept similarities between sonar and ultrasound systems are analyzed in order to exploit the use of model-based sonar signal processing concepts in ultrasound problems. The discussion on model-based signal processing is extended in Chapter 5 to determine the most appropriate signal processing approaches for measurements that are contaminated with noise and under lying uncertainties. In general, if the SNR of the measurements is high, then simple non-physical tech niques such as Fourier transform-based temporal and spatial processing schemes can be used to extract the desired information. However, if the SNR is extremely low and/or the propagation medium is uncertain, then more of the underlying propagation physics must be incorporated somehow into the processor to extract the information. These are issues that are discussed in Chapter 5, which introduces a generic development of model-based processing schemes and then concentrates specifically on those designed for sonar system applications.
- 30. Processing Concept Similarities among Sonar, Radar, and Medical Systems 15 Thus, Chapters 2, 3, 4, 5, 6, and 11 address a major issue: the implementation of advanced processing schemes in real-time systems of interest. The starting point will be to identify the signal processing concept similarities among radar, sonar, and medical imaging systems by defining a generic signal processing structure integrating the processing functionalities of the real-time systems of interest. The definition of a generic signal processing structure for a variety of systems will address the above continuing interest that is supported by the fact that synthetic aperture and adaptive processing techniques provide new gain.2’1 5 ’20’21’23 This kind of improvement in array gain is equivalent to improvements in system performance. In general, improvements in system performance or array gain improvements are required when the noise environment of an operational system is non-isotropic, such as the noise environment of ( 1) atmospheric noise or clutter (radar applications), (2) cluttered coastal waters and areas with high shipping density in which sonar systems operate (sonar applications), and (3) the complexity of the human body (medical imaging applications). An alternative approach to improve the array gain of a real-time system requires the deployment of very large aperture arrays, which leads to technical and operational implica tions. Thus, the implementation of non-conventional signal processing schemes in operational systems will minimize very costly H/W requirements associated with array gain improvements. Figure 1.2 shows the configuration of a generic signal processing scheme integrating the functionality of radar, sonar, ultrasound, medical tomography CT/X-ray, and magnetic resonance imaging (MRI) systems. There are five major and distinct processing blocks in the generic structure. Moreover, recon figuration of the different processing blocks of Figure 1.2 allows the application of the proposed concepts to a variety of active or passive digital signal processing (DSP) systems. The first point of the generic processing flow configuration is that its implementation is in the frequency domain. The second point is that with proper selection of filtering weights and careful data partitioning, the frequency domain outputs of conventional or advanced processing schemes can be made equivalent to the FFT of the broadband outputs. This equivalence corresponds to implementing finite impulse response (FIR) filters via circular convolution with the FFT, and it allows spatial-temporal processing of narrowband and broadband types of signals,2’1 5’30 as defined in Chapter 6. Thus, each processing block in the generic DSP structure provides continuous time series; this is the central point of the implementation concept that allows the integration of quite diverse processing schemes, such as those shown in Figure 1.2. More specifically, the details of the generic processing flow of Figure 1.2 are discussed very briefly in the following sections. 1.3.1 Signal Conditioning of Array Sensor Time Series The block titled Signal Conditioning for Array Sensor Time Series in Figure 1.2 includes the partitioning of the time series from the receiving sensor array, their initial spectral FFT, the selection of the signal’s frequency band of interest via bandpass FIR filters, and downsampling. The output of this block provides continuous time series at a reduced sampling rate for improved temporal spectral resolution. In many system applica tions including moving arrays of sensors, array shape estimation or the sensor coordinates would be required to be integrated with the signal processing functionality of the system, as shown in this block. Typical system requirements of this kind are towed array sonars,1 5which are discussed in Chapters 6, 10, and 11; CT/X-ray tomography systems,6-8 which are analyzed in Chapters 15 and 16; and ultrasound imaging systems deploying long line or planar arrays,8-10which are discussed in Chapters 6, 7,13, and 14. The processing details of this block will be illustrated in schematic diagrams in Chapter 6. The FIR band selection processing of this block is typical in all the real-time systems of interest. As a result, its output can be provided as input to the blocks named Sonar, Radar & Ultrasound Systems or Tomography Imaging Systems. 1.3.2 Tomography Imaging CT/X-Ray and MRI Systems The block at the right-hand side of Figure 1.2, which is titled Tomography Imaging Systems, includes image reconstruction algorithms for medical imaging CT/X-ray and MRI systems. The processing details of these
- 31. 1-6 Advanced Signal Processing Handbook FIGURE 1.2 A generic signal processing structure integrating the signal processing functionalities of sonar, radar, ultrasound, CT/X-ray, and MRI medical imaging systems. algorithms will be discussed in Chapters 15 through 17. In general, image reconstruction algorithms6,7,11-13 are distinct processing schemes, and their implementation is practically efficient in CT and MRI applications. However, tomography imaging and the associated image reconstruction algorithms can be applied in other system applications such as diffraction tomography using ultrasound sources8and acoustic tomography of the ground using various acoustic frequency regimes. Diffraction tomography is not practical for medical
- 32. Processing Concept Similarities among Sonar, Radar, Medical Systems 1-7 imaging applications because of the very poor image resolution and the very high absorption rate of the acoustic energy by the bone structure of the human body. In geophysical applications, however, seismic waves can be used in tomographic imaging procedures to detect and classify very large buried objects. On the other hand, in working with higher acoustic frequencies, a better image resolution would allow detection and classification of small, shallow buried objects such as anti-personnel land mines,4 1 which is a major humanitarian issue that has attracted the interest of U.N. and the highly industrialized countries in North America and Europe. The rule of thumb in acoustic tomography imaging applications is that higher frequency regimes in radiated acoustic energy would provide better image resolution at the expense of higher absorption rates for the radiated energy penetrating the medium of interest. All these issues and the relevant industrial applications of computed tomography imaging are discussed in Chapter 15. 1.3.3 Sonar, Radar, and Ultrasound Systems The underlying signal processing functionality in sonar, radar, and modern ultrasound imaging systems deploying linear, planar, cylindrical, or spherical arrays is beamforming. Thus, the block in Figure 1.2 titled Sonary Radar & Ultrasound Systems includes such sub-blocks as FIR Filter/Conventional Beam form ing and FIR Filter/Adaptive & Synthetic Aperture Beamforming for multi-dimensional arrays with linear, planar, circular, cylindrical, and spherical geometric configurations. The output of this block provides continuous, directional beam time series by using the FIR implementation scheme of the spatial filtering via circular convolution. The segmentation and overlap of the time series at the input of the beamformers take care of the wraparound errors that arise in fast-convolution signal processing operations. The overlap size is equal to the effective FIR filters length.1530 Chapter 6 will discuss in detail the conventional, adaptive, and sythetic aperture beamformers that can be implemented in this block of the generic processing structure in Figure 1.2. Moreover, Chapters 6 and 11 provide some real data output results from sonar systems deploying linear or cylindrical arrays. 1.3.4 Active and Passive Systems The blocks named Passive and Active in the generic structure of Figure 1.2 are the last major processes that are included in most of the DSP systems. Inputs to these blocks are continuous beam time series, which are the outputs of the conventional and advanced beamformers of the previous block. However, continuous sensor time series from the first block titled Signal Conditioning fo r Array Sensor Time Series can be provided as the input of the Active and Passive blocks for temporal spectral analysis. The block titled Active includes a M atched Filter sub-block for the processing of active signals. The option here is to include the mediums propagation characteristics in the replica of the active signal considered in the matched filter in order to improve detection and gain.1536 The sub-blocks Ver- nier/Band Form ation NB (Narrowband) Analysis, and BB (Broadband) Analysis include the final processing steps of a temporal spectral analysis for the beam time series. The inclusion of the Vernier sub-block is to allow the option for improved frequency resolution. Chapter 11 discusses the signal processing functionality and system-oriented applications associated with active and passive sonars. Furthermore, Chapter 13 extends the discussion to address the signal processing issues relevant with ultrasound medical imaging systems. In summary, the strength of the generic processing structure in Figure 1.2 is that it identifies and exploits the processing concept similarities among radar, sonar, and medical imaging systems. Moreover, it enables the implementation of non-linear signal processing methods, adaptive and synthetic aperture, as well as the equivalent conventional approaches. This kind of parallel functionality for conventional and advanced processing schemes allows for a very cost-effective evaluation of any type of improvement during the concept demonstration phase. As stated above, the derivation of the effective filter length of an FIR adaptive and synthetic aperture filtering operation is very essential for any type of application that will allow simultaneous NB and BB signal processing. This is a non-trivial problem because of the dynamic characteristics of the adaptive algorithms, and it has not as yet been addressed.
- 33. 1-8 Advanced Signal Processing Handbook In the past, attempts to implement matrix-based signal processing methods such as adaptive processing were based on the development of systolic array H/W because systolic arrays allow large amounts of parallel computation to be performed efficiently since communications occur locally. Unfortunately, systolic arrays have been much less successful in practice than in theory. Systolic arrays big enough for real problems cannot fit on one board, much less on one chip, and interconnects have problems. A two- dimensional (2-D) systolic array implementation will be even more difficult. Recent announcements, however, include successful developments of super-scalar and massively parallel signal processing com puters that have throughput capabilities of hundred of billions of GFLOPS.40 It is anticipated that these recent computing architecture developments would address the computationally intensive scalar and matrix-based operations of advanced signal processing schemes for next-generation real-time systems. Finally, the block Data Manager in Figure 1.2 includes the display system, normalizers, target motion analysis, image post-processing, and OR-ing operations to map the output results into the dynamic range of the display devices. This will be discussed in the next section. 1.4 Data Manager and Display Sub-System Processed data at the output of the mainstream signal processing system must be stored in a temporary database before they are presented to the system operator for analysis. Until very recently, owing to the physical size and cost associated with constructing large databases, the data manager played a relatively small role in the overall capability of the aforementioned systems. However, with the dramatic drop in the cost of solid-state memories and the introduction of powerful microprocessors in the 1980s, the role of the data manager has now been expanded to incorporate post-processing of the signal processor’s output data. Thus, post-processing operations, in addition to the traditional display data management functions, may include • For sonar and radar systems • Normalization and OR-ing • Signal tracking • Localization • Data fusion • Classification functionality • For medical imaging systems • Image post-processing • Normalizing operations • Registration and image fusion It is apparent from the above discussion that for a next-generation DSP system, emphasis should be placed on the degree of interaction between the operator and the system through an operator-machine interface (OMI), as shown schematically in Figure 1.1. Through this interface, the operator may selectively proceed with localization, tracking, diagnosis, and classification tasks. A high-level view of the generic requirements and the associated technologies of the data manager of a next-generation DSP system reflecting the above concerns could be as shown in Figure 1.3. The central point of Figure 1.3 is the operator that controls two kinds of displays (the processed information and tactical displays) through a continuous interrogation procedure. In response to the operator’s request, the units in the data manager and display sub-system have a continuous interaction including data flow and requests for processing that include localization, tracking, classification for sonar-radar systems (Chapters 8 and 9), and diagnostic images for medical imaging systems (Chapter 7). Even though the processing steps of radar and airborne systems associated with localization, tracking, and classification have conceptual similarities with those of a sonar system, the processing techniques that have been successfully applied in airborne systems have not been successful with sonar systems. This
- 34. Processing Concept Similarities among Sonar, Radar, and Medical Systems 1-9 DISPLAY SUB-SYSTEM FIGURE 1.3 Schematic diagram for the generic requirements of a data manager for a next-generation, real-time DSP system. is a typical situation that indicates how hostile, in terms of signal propagation characteristics, the underwater environment is with respect to the atmospheric environment. However, technologies associated with data fusion, neural networks, knowledge-based systems, and autom ated param eter esti mation will provide solutions to the very difficult operational sonar problem regarding localization, tracking, and classification. These issues are discussed in detail in Chapters 8 and 9. In particular, Chapter 8 focuses on target tracking and sensor data processing for active sensors. Although active sensors certainly have an advantage over passive sensors, nevertheless, passive sensors may be prereq uisite to some tracking solution concepts, namely, passive sonar systems. Thus, Chapter 9 deals with a class of tracking problems for passive sensors only. 1.4.1 Post-Processing for Sonar and Radar Systems To provide a better understanding of these differences, let us examine the levels of information required by the data management of sonar and radar systems. Normally, for sonar and radar systems, the processing and integration of information from sensor level to a command and control level include a few distinct processing steps. Figure 1.4 shows a simplified overview of the integration of four different levels of information for a sonar or radar system. These levels consist mainly of • Navigation and non-sensor array data • Environmental information and estimation of propagation characteristics in order to assess the mediums influence on sonar or radar system performance • Signal processing of received sensor signals that provide parameter estimation in terms of bearing, range, and temporal spectral estimates for detected signals • Signal following (tracking) and localization that monitors the time evolution of a detected signals estimated parameters
- 35. 1-10 Advanced Signal Processing Handbook FIGURE 1.4 A simplified overview of integration of different levels of information from the sensor level to a command and control level for a sonar or radar system. These levels consist mainly of (1) navigation; (2) environ mental information to access the medium’s influence on sonar or radar system performance; (3) signal processing of received array sensor signals that provides parameter estimation in terms of bearing, range, and temporal spectral estimates for detected signals; and (4) signal following (tracking) and localization of detected targets. (Reprinted by permission of IEEE ©1998.)
- 36. Processing Concept Similarities among Sonar, Radar, and Medical Systems M l This last tracking and localization capability32,33allows the sonar or radar operator to rapidly assess the data from a multi-sensor system and carry out the processing required to develop an array sensor-based tactical picture for integration into the platform level command and control system, as shown later by Figure 1.9. In order to allow the databases to be searched effectively, a high-performance OMI is required. These interfaces are beginning to draw heavily on modern workstation technology through the use of windows, on-screen menus, etc. Large, flat panel displays driven by graphic engines which are equally adept at pixel manipulation as they are with 3-D object manipulation will be critical components in future systems. It should be evident by now that the term data manager describes a level of functionality which is well beyond simple data management. The data manager facility applies technologies ranging from relational databases, neural networks,26 and fuzzy systems27 to expert systems.15,26 The problems it addresses can be variously characterized as signal, data, or information processing. 1.4.2 Post-Processing for Medical Imaging Systems Let us examine the different levels of information to be integrated by the data manager of a medical imaging system. Figure 1.5 provides a simplified overview of the levels of information to be integrated by a current medical imaging system. These levels include • The system structure in terms of array-sensor configuration and computing architecture • Sensor time series signal processing structure • Image processing structure • Post-processing for reconstructed image to assist medical diagnosis In general, current medical imaging systems include very limited post-processing functionality to enhance the images that may result from mainstream image reconstruction processing. It is anticipated, however, that next-generation medical imaging systems will enhance their capabilities in post-processing functionality by including image post-processing algorithms that are discussed in Chapters 7 and 14. More specifically, although modern medical imaging modalities such as CT, MRA, MRI, nuclear medicine, 3-D ultrasound, and laser con-focal microscopy provide “slices of the body,” significant dif ferences exist between the image content of each modality. Post-processing, in this case, is essential with special emphasis on data structures, segmentation, and surface- and volume-based rendering for visual izing volumetric data. To address these issues, the first part of Chapter 7 focuses less on explaining algorithms and rendering techniques, but rather points out their applicability, benefits, and potential in the medical environment. Moreover, in the second part of Chapter 7, applications are illustrated from the areas of craniofacial surgery, traumatology, neurosurgery, radiotherapy, and medical education. Furthermore, some new applications of volumetric methods are presented: 3-D ultrasound, laser con- focal data sets, and 3D-reconstruction of cardiological data sets, i.e., vessels as well as ventricles. These new volumetric methods are currently under development, but due to their enormous application potential they are expected to be clinically accepted within the next few years. As an example, Figures 1.6 and 1.7 present the results of image enhancement by means of post processing on images that have been acquired by current CT/X-ray and ultrasound systems. The left- hand-side image of Figure 1.6 shows a typical X-ray image of a human skull provided by a current type of CT/X-ray imaging system. The right-hand-side image of Figure 1.6 is the result of post-processing the original X-ray image. It is apparent from these results that the right-hand-side image includes imaging details that can be valuable to medical staff in minimizing diagnostic errors and interpreting image results. Moreover, this kind of post-processing image functionality may assist in cognitive operations associated with medical diagnostic applications. Ultrasound medical imaging systems are characterized by poor image resolution capabilities. The three images in Figure 1.7 (top left and right images, bottom left-hand-side image) provide pictures of the skull of a fetus as provided by a conventional ultrasound imaging system. The bottom right-hand-side image of Figure 1.7 presents the resulting 3-D post-processed image by applying the processing algorithms discussed in Chapter 7. The 3-D features and characteristics of the skull of the fetus are very pronounced in this case,
- 37. 1-12 Advanced Signal Processing Handbook FIGURE 1.5 A simplified overview of the integration of different levels of information from the sensor level to a command and control level for a medical imaging system. These levels consist mainly of (1) sensor array configuration, (2) computing architecture, (3) signal processing structure, and (4) reconstructed image to assist medical diagnosis.
- 38. Processing Concept Similarities among Sonar, Radar, and Medical Systems 1-13 FIGURE 1.6 The left-hand-side is an X-ray image of a human skull. The right-hand-side image is the result of image enhancement by means of post-processing the original X-ray image. (Courtesy of Prof. G. Sakas, Fraunhofer IDG, Durmstadt, Germany.) FIGURE 1.7 The two top images and the bottom left-hand-side image provide details of a fetus’ skull using convetional medical ultrasound systems. The bottom right-hand-side 3-D image is the result of image enhancement by means of post-processing the original three ultrasound images. (Courtesy of Prof. G. Sakas, Fraunhofer IDG, Durmstadt, Germany.)
- 39. 1-14 Advanced Signal Processing Handbook although the clarity is not as good as in the case of the CT/X-ray image in Figure 1.6. Nevertheless, the image resolution characteristics and 3-D features that have been reconstructed in both cases, shown in Figures 1.6 and 1.7, provide an example of the potential improvements in the image resolution and cognitive functionality that can be integrated in the next-generation medical imaging systems. Needless to say, the image post-processing functionality of medical imaging systems is directly appli cable in sonar and radar applications to reconstruct 2-D and 3-D image details of detected targets. This kind of image reconstruction post-processing capability may improve the difficult classification tasks of sonar and radar systems. At this point, it is also important to re-emphasize the significant differences existing between the image content and system functionality of the various medical imaging systems mainly in terms of sensor-array configuration and signal processing structures. Undoubtedly, a generic approach exploiting the concep tually similar processing functionalities among the various configurations of medical imaging systems will simplify OMI issues that would result in better interpretation of information of diagnostic impor tance. Moreover, the integration of data fusion functionality in the data manager of medical imaging systems will provide better diagnostic interpretation of the information inherent at the output of the medical imaging systems by minimizing human errors in terms of interpretation. Although these issues may appear as exercises of academic interest, it becomes apparent from the above discussion that system advances made in the field of sonar and radar systems may be applicable in medical imaging applications as well. 1.4.3 Signal and Target Tracking and Target Motion Analysis In sonar, radar, and imaging system applications, single sensors or sensor networks are used to collect information on time-varying signal parameters of interest. The individual output data produced by the sensor systems result from complex estimation procedures carried out by the signal processor introduced in Section 1.3 (sensor signal processing). Provided the quantities of interest are related to moving point-source objects or small extended objects (radar targets, for instance), relatively simple statistical models can often be derived from basic physical laws, which describe their temporal behavior and thus define the underlying dynamical system. The formulation of adequate dynamics models, however, may be a difficult task in certain applications. For an efficient exploitation of the sensor resources as well as to obtain information not directly provided by the individual sensor reports, appropriate data association and estimation algorithms are required (sensor data processing). These techniques result in tracks, i.e., estimates of state trajectories, which statistically represent the quantities or objects considered along with their temporal history. Tracks are initiated, confirmed, maintained, stored, evaluated, fused with other tracks, and displayed by the tracking system or data manager. The tracking system, however, should be carefully distinguished from the underlying sensor systems, though there may exist close interrelations, such as in the case of multiple target tracking with an agile-beam radar, increasing the complexity of sensor management. In contrast to the target tracking via active sensors, discussed in Chapter 8, Chapter 9 deals with a class of tracking problems that use passive sensors only. In solving tracking problems, active sensors certainly have an advantage over passive sensors. Nevertheless, passive sensors may be a prerequisite to some tracking solution concepts. This is the case, e.g., whenever active sensors are not feasible from a technical or tactical point of view, as in the case of passive sonar systems deployed by submarines and surveillance naval vessels. An important problem in passive target tracking is the target motion analysis (TMA) problem. The term TMA is normally used for the process of estimating the state of a radiating target from noisy measurements collected by a single passive observer. Typical applications can be found in passive sonar, infrared (IR), or radar tracking systems. For signal followers, the parameter estimation process for tracking the bearing and frequency of detected signals consists of peak picking in a region of bearing and frequency space sketched by fixed gate sizes at the outputs of the conventional and non-conventional beamformers depicted in Figure 1.2. Figure 1.8 provides a schematic interpretation of the signal followers functionality in tracking the time-varying frequency and bearing estimates of detected signals in sonar and radar applications. Details about this
- 40. Processing Concept Similarities among Sonar, Radar, and Medical Systems 1-15 FIGURE 1.8 Signal following functionality in tracking the time-varying frequency and bearing of a detected signal (target) by a sonar or radar system. (Courtesy of William Cambell, Defence Research Establishment Atlantic, Dart mouth, NS, Canada.) estimation process can be found in Reference 34 and in Chapters 8 and 9 of this handbook. Briefly, in Figure 1.8, the choice of the gate sizes was based on the observed bearing and frequency fluctuations of a detected signal of interest during the experiments. Parabolic interpolation was used to provide refined bearing estimates.35 For this investigation, the bearings-only tracking process described in Reference 34 was used as an NB tracker, providing unsmoothed time evolution of the bearing estimates to the localization process.3236 Tracking of the time-varying bearing estimates of Figure 1.8 forms the basic processing step to localize a distant target associated with the bearing estimates. This process is called localization or TMA, which is discussed in Chapter 9. The output results of a TMA process form the tactical display of a sonar or radar system, as shown in Figures 1.4 and 1.8. In addition, the temporal-spatial spectral analysis output results and the associated display (Figures 1.4 and 1.8) form the basis for classification and the target identification process for sonar and radar systems. In particular, data fusion of the TMA output results with those of temporal-spatial spectral analysis output results outline an integration process to define the tactical picture for sonar and radar operations, as shown in Figure 1.9. For more details, the reader is referred to Chapters 8 and 9, which provide detailed discussions of target tracking and TMA operations for sonar and radar systems.32-36 It is apparent from the material presented in this section that for next-generation sonar and radar systems, emphasis should be placed on the degree of interaction between the operator and the system, through an OMI as shown schematically in Figures 1.1 and 1.3. Through this interface, the operator may selectively proceed with localization, tracking, and classification tasks, as depicted in Figure 1.7. In standard computed tomography (CT), image reconstruction is performed using projection data that are acquired in a time sequential manner.6,7 Organ motion (cardiac motion, blood flow, lung motion due to respiration, patients restlessness, etc.) during data acquisition produces artifacts, which appear as a blurring effect in the reconstructed image and may lead to inaccurate diagnosis.1 4 The intuitive solution to this problem is to speed up the data acquisition process so that the motion effects become negligible. However, faster CT scanners tend to be significantly more costly, and, with current X-ray tube technology, the scan times that are required are simply not realizable. Therefore, signal processing algorithms to account for organ motion artifacts are needed. Several mathematical techniques have been proposed as a solution
- 41. 1-16 Advanced Signal Processing Handbook FIGURE 1.9 Formation of a tactical picture for sonar and radar systems. The basic operation is to integrate by means of data fusion the signal tracking and localization functionality with the temporal-spatial spectral analysis output results of the generic signal processing structure of Figure 1.2. (Courtesy of Dr. William Roger, Defence Research Establishment Atlantic, Dartmouth, NS, Canada.) to this problem. These techniques usually assume a simplistic linear model for the motion, such as translational, rotational, or linear expansion.14 Some techniques model the motion as a periodic sequence and take projections at a particular point in the motion cycle to achieve the effect of scanning a stationary object. This is known as a retrospective electrocardiogram (ECG)-gating algorithm, and projection data are acquired during 12 to 15 continuous 1-s source rotations while cardiac activity is recorded with an ECG. Thus, the integration of ECG devices with X-ray CT medical tomography imaging systems becomes a necessity in cardiac imaging applications using X-ray CT and MRI systems. However, the information provided by the ECG devices to select in-phase segments of CT projection data can be available by signal trackers that can be applied on the sensor time series of the CT receiving array. This kind of application of signal trackers on CT sensor time series will identify the in-phase motion cycles of the heart under a similar configuration as the ECG-gating procedure. Moreover, the application of the signal trackers in cardiac CT imaging systems will eliminate the use of the ECG systems, thus making the medical imaging operations much simpler. These issues will be discussed in some detail in Chapter 16. It is anticipated, however, that radar, sonar, and medical imaging systems will exhibit fundamental differences in their requirements for information post-processing functionality. Furthermore, bridging conceptually similar processing requirements may not always be an optimum approach in addressing practical DSP implementation issues; rather it should be viewed as a source of inspiration for the researchers in their search for creative solutions. In summary, past experience in DSP system development that “improving the signal processor of a sonar or radar or medical imaging system was synonymous with the development of new signal processing algorithms and faster hardware” has changed. While advances will continue to be made in these areas, future developments in data (contact) management represent one of the most exciting avenues of research in the development of high-performance systems.
- 42. Processing Concept Similarities among Sonar, Radar, and Medical Systems 1-17 In sonar, radar, and medical imaging systems, an issue of practical importance is the operational requirement by the operator to be able to rapidly assess numerous images and detected signals in terms of localization, tracking, classification, and diagnostic interpretation in order to pass the necessary information up through the chain of command to enable tactical or medical diagnostic decisions to be made in a timely manner. Thus, an assigned task for a data manager would be to provide the operator with quick and easy access to both the output of the signal processor, which is called processed data display, and the tactical display, which will show medical images and localization and tracking information through graphical interaction between the processed data and tactical displays. 1.4.4 Engineering Databases The design and integration of engineering databases in the functionality of a data manager assist the identification and classification process, as shown schematically in Figure 1.3. To illustrate the concept of an engineering database, we will consider the land mine identification process, which is a highly essential functionality in humanitarian demining systems to minimize the false alarm rate. Although a lot of information on land mines exists, often organized in electronic databases, there is nothing like a CAD engineering database. Indeed, most databases serve either documentation purposes or are land mine signatures related to a particular sensor technology. This wealth of information must be collected and organized in such a way so that it can be used online, through the necessary interfaces to the sensorial information, by each one of the future identification systems. Thus, an engineering database is intended to be the common core software applied to all future land mine detection systems.41 It could be built around a specially engineered database storing all available information on land mines. The underlying idea is, using techniques of cognitive and perceptual sciences, to extract the particular features that characterize a particular mine or a class of mines and, successively, to define the sensorial information needed to detect these features in typical environments. Such a land mine identification system would not only trigger an alarm for every suspect object, but would also reconstruct a comprehensive model of the target. Successively, it would compare the model to an existing land mine engineering database deciding or assisting the operator to make a decision as to the nature of the detected object. A general approach of the engineering database concept and its applicability in the aforementioned DSP systems would assume that an effective engineering database will be a function of the available information on the subjects of interest, such as underwater targets, radar targets, and medical diagnostic images. Moreover, the functionality of an engineering database would be highly linked with the multi sensor data fusion process, which is the subject of discussion in the next section. 1.4.5 Multi-Sensor Data Fusion Data fusion refers to the acquisition, processing, and synergistic combination of information from various knowledge sources and sensors to provide a better understanding of the situation under consideration.39 Classification is an information processing task in which specific entities are mapped to general categories. For example, in the detection of land mines, the fusion of acoustic,41 electromagnetic (EM), and IR sensor data is in consideration to provide a better land mine field picture and minimize the false alarm rates. The discussion of this section has been largely influenced by the work of Kundur and Hatzinakos39 on “Blind Image Deconvolution” (for more details the reader is referred to Reference 39). The process of multi-sensor data fusion addresses the issue of system integration of different type of sensors and the problems inherent in attempting to fuse and integrate the resulting data streams into a coherent picture of operational importance. The term integration is used here to describe operations wherein a sensor input may be used independently with respect to other sensor data in structuring an overall solution. Fusion is used to describe the result of joint analysis of two or more originally distinct data streams.
- 43. 1-18 Advanced Signal Processing Handbook More specifically, while multi-sensors are more likely to correctly identify positive targets and eliminate false returns, using them effectively will require fusing the incoming data streams, each of which may have a different character. This task will require solutions to the following engineering problems: • Correct combination of the multiple data streams in the same context • Processing multiple signals to eliminate false positives and further refine positive returns For example, in humanitarian demining, a positive return from a simple metal detector might be combined with a ground penetrating radar (GPR) evaluation, resulting in the classification of the target as a spent shell casing and allowing the operator to safely pass by in confidence. Given a design that can satisfy the above goals, it will then be possible to design and implement computer-assisted or automatic recognition in order to positively identify the nature, position, and orientation of a target. Automatic recognition, however, will be pursued by the engineering database, as shown in Figure 1.3. In data fusion, another issue of equal importance is the ability to deal with conflicting data, producing interim results that the algorithm can revise as more data become available. In general, the data interpretation process, as part of the functionality of data fusion, consists briefly of the following stages:39 • Low-level data manipulation • Extraction of features from the data either using signal processing techniques or physical sensor models • Classification of data using techniques such as Bayesian hypothesis testing, fuzzy logic, and neural networks • Heuristic expert system rules to guide the previous levels, make high-level control decisions, provide operator guidance, and provide early warnings and diagnostics Current research and development (R&D) projects in this area include the processing of localization and identification of data from various sources or type of sensors. The systems combine features of modern multi-hypothesis tracking methods and correlation. This approach, to process all available data regarding targets of interest, allows the user to extract the maximum amount of information concerning target location from the complex “sea” of available data. Then a correlation algorithm is used to process large volumes of data containing localization and to attribute information using multiple hypothesis methods. In image classification and fusion strategies, many inaccuracies often result from attempting to fuse data that exhibit motion-induced blurring or defocusing effects and background noise.37,38Compensation for such distortions is inherently sensor dependent and non-trivial, as the distortion is often time varying and unknown. In such cases, blind image processing, which relies on partial information about the original data and the distorting process, is suitable.39 In general, multi-sensor data fusion is an evolving subject, which is considered to be highly essential in resolving the sonar, radar detection/classification, and diagnostic problems in medical imaging systems. Since a single sensor system with an acceptable very low false alarm rate is rarely available, current developments in sonar, radar, and medical imaging systems include multi-sensor configura tions to minimize the false alarm rates. Then the multi-sensor data fusion process becomes highly essential. Although data fusion and databases have not been implemented yet in medical imaging systems, their potential use in this area will undoubtedly be a rapidly evolving R&D subject in the near future. Then system experience in the areas of sonar and radar systems would be a valuable asset in that regard. For medical imaging applications, the data and image fusion processes will be discussed in detail in Chapter 19. Finally, Chapter 20 concludes the material of this handbook by providing clinical data and discussion on the role of medical imaging in radiotherapy treatment planning.
- 44. Processing Concept Similarities among Sonar, Radar, and Medical Systems 1-19 References 1. W.C. Knight, R.G. Pridham, and S.M. Kay, Digital signal processing for sonar, Proc. IEEE, 69(11), 1451-1506, 1981. 2. B. Windrow et al., Adaptive antenna systems, Proc. IEEE, 55(12), 2143-2159, 1967. 3. B. Windrow and S.D. Stearns, Adaptive Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1985. 4. A. A. Winder, Sonar system technology, IEEE Trans. Sonic Ultrasonics, SU-22(5), 291-332, 1975. 5. A.B. Baggeroer, Sonar signal processing, in Applications o f Digital Signal Processing, A.V. Oppen- heim, Ed., Prentice-Hall, Englewood Cliffs, NJ, 1978. 6. H.J. Scudder, Introduction to computer aided tomography, Proc. IEEE, 66(6), 628-637, 1978. 7. A.C. Kak and M. Slaney, Principles o f Computerized Tomography Imaging, IEEE Press, New York, 1992. 8. D. Nahamoo and A.C. Kak, Ultrasonic Diffraction Imaging, TR-EE 82-80, Department of Electrical Engineering, Purdue University, West Lafayette, IN, August 1982. 9. S.W. Flax and M. O’Donnell, Phase-aberration correction using signals from point reflectors and diffuse scatterers: basic principles, IEEE Trans. Ultrasonics, Ferroelectrics Frequency Control, 35(6), 758-767, 1988. 10. G.C. Ng, S.S. Worrell, P.D. Freiburger, and G.E. Trahey, A comparative evaluation of several algorithms for phase aberration correction, IEEE Trans. Ultrasonics, Ferroelectrics Frequency Con trol, 41(5), 631-643, 1994. 11. A.K. Jain, Fundamentals o f Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1990. 12. Q.S. Xiang and R.M. Henkelman, K-space description for the imaging of dynamic objects, Magn. Reson. Med., 29, 422-428, 1993. 13. M.L. Lauzon, D.W. Holdsworth, R. Frayne, and B.K. Rutt, Effects of physiologic waveform vari ability in triggered MR imaging: theoretical analysis, /. Magn. Reson. Imaging, 4(6), 853-867,1994. 14. C.J. Ritchie, C.R. Crawford, J.D. Godwin, K.F. King, and Y. Kim, Correction of computed tomog raphy motion artifacts using pixel-specific back-projection, IEEE Trans. M edical Imaging, 15(3), 333-342, 1996. 15. S. Stergiopoulos, Implementation of adaptive and synthetic-aperture processing schemes in inte grated active-passive sonar systems, Proc. IEEE, 86(2), 358— 396, 1998. 16. D. Stansfield, Underwater Electroacoustic Transducers, Bath University Press and Institute of Acous tics, 1990. 17. J.M. Powers, Long range hydrophones, in Applications o f Ferroelectric Polymers, T.T. Wang, J.M. Herbert, and A.M. Glass, Eds., Chapman & Hall, New York, 1988. 18. P.B. Boemer, W.A. Edelstein, C.E. Hayes, S.P. Souza, and O.M. Mueller, The NMR phased array, Magn. Reson. Med., 16, 192-225, 1990. 19. P.S. Melki, F.A. Jolesz, and R.V. Mulkern, Partial RF echo planar imaging with the FAISE method. I. Experimental and theoretical assessment of artifact, Magn. Reson. Med., 26, 328-341, 1992. 20. N.L. Owsley, Sonar Array Processing, S. Haykin, Ed., Signal Processing Series, A.V. Oppenheim, Series Ed., p. 123, Prentice-Hall, Englewood Cliffs, NJ, 1985. 21. B. Van Veen and K. Buckley, Beamforming: a versatile approach to spatial filtering, IEEE ASSP Mag., 4-24, 1988. 22. A.H. Sayed and T. Kailath, A state-space approach to adaptive RLS filtering, IEEE SP Mag., July, 18-60, 1994. 23. E.J. Sullivan, W.M. Carey, and S. Stergiopoulos, Editorial special issue on acoustic synthetic aperture processing, IEEE J. Oceanic Eng., 17(1), 1-7, 1992. 24. C.L. Nikias and J.M. Mendel, Signal processing with higher-order spectra, IEEE SP Mag., July, 10-37, 1993. 25. S. Stergiopoulos and A.T. Ashley, Guest Editorial for a special issue on sonar system technology, IEEE J. Oceanic Eng., 18(4), 361-365, 1993.
- 45. 1-20 Advanced Signal Processing Handbook 26. A.B. Baggeroer, W.A. Kuperman, and P.N. Mikhalevsky, An overview of matched field methods in ocean acoustics, IEEE J. Oceanic Eng., 18(4), 401-424, 1993. 27. “Editorial” special issue on neural networks for oceanic engineering systems, IEEE J. Oceanic Eng., 17, 1-3, October 1992. 28. A. Kummert, Fuzzy technology implemented in sonar systems, IEEE J. Oceanic Eng., 18(4), 483-490, 1993. 29. R.D. Doolitle, A. Tolstoy, and E.J. Sullivan, Editorial special issue on detection and estimation in matched field processing, IEEE J. Oceanic Eng., 18, 153-155, 1993. 30. A. Antoniou, Digital Filters: Analysis, Design, and Applications, 2nd Ed., McGraw-Hill, New York, 1993. 31. Mercury Computer Systems, Inc., Mercury News }an-97, Mercury Computer Systems, Inc., Chelms ford, MA, 1997. 32. Y. Bar-Shalom and T.E. Fortman, Tracking and Data Association, Academic Press, Boston, MA, 1988. 33. S.S. Blackman, Multiple-Target Tracking with Radar Applications, Artech House Inc., Norwood, MA, 1986. 34. W. Cambell, S. Stergiopoulos, and J. Riley, Effects of bearing estimation improvements of non- conventional beamformers on bearing-only tracking, Proc. Oceans ’95 MTS/IEEE, San Diego, CA, 1995. 35. W.A. Roger and R.S. Walker, Accurate estimation of source bearing from line arrays, Proc. Thirteen Biennial Symposium on Communications, Kingston, Ontario, Canada, 1986. 36. D. Peters, Long Range Towed Array Target Analysis — Principles and Practice, DREA Memoran dum 95/217, Defence Research Establishment Atlantic, Dartmouth, NS, Canada, 1995. 37. A.H.S. Solberg, A.K. Jain, and T. Taxt, A Markov random field model for classification of multi source satellite imagery, IEEE Trans. Geosci. Remote Sensing, 32, 768-778, 1994. 38. L.J. Chipman et al., Wavelets and image fusion, Proc. SPIE, 2569, 208-219, 1995. 39. D. Kundur and D. Hatzinakos, Blind image deconvolution, Signal Processing Magazine, 13, 43-64, May 1996. 40. Mercury Computer Systems, Inc., Mercury News Jan-98, Mercury Computer Systems, Inc., Chelms ford, MA, 1998. 41. S. Stergiopoulos, R. Alterson, D. Havelock, and J. Grodski, Acoustic Tomography Methods for 3D Imaging of Shallow Buried Objects, 139th Meeting of the Acoustical Society of America, Atlanta, GA, May 2000.
- 46. 2 Adaptive Systems for Signal Process* Simon Haykin 2.1 The Filtering Problem.................................................................2-1 McMaster University 2.2 Adaptive Filters............................................................................. 2-2 2.3 Linear Filter Structures............................................................. 2-4 Transversal Filter •Lattice Predictor •Systolic Array 2.4 Approaches to the Development of Linear Adaptive Filtering Algorithms.................................................................... 2-8 Stochastic Gradient Approach • Least-Squares Estimation •How to Choose an Adaptive Filter 2.5 Real and Complex Forms of Adaptive Filters...................2-13 2.6 Nonlinear Adaptive Systems:Neural Networks................. 2-14 Supervised Learning • Unsupervised Learning •Information- Theoretic Models •Temporal Processing Using Feedforward Networks •Dynamically Driven Recurrent Networks 2.7 Applications.................................................................................2-24 System Identification • Spectrum Estimation •Signal Detection •Target Tracking •Adaptive Noise Canceling •Adaptive Beamforming 2.8 Concluding Remarks.................................................................2-45 References................................................................................................2-46 2.1 The Filtering Problem The term “filter” is often used to describe a device in the form of a piece of physical hardware or software that is applied to a set of noisy data in order to extract information about a prescribed quantity of interest. The noise may arise from a variety of sources. For example, the data may have been derived by means of noisy sensors or may represent a useful signal component that has been corrupted by transmission through a communication channel. In any event, we may use a filter to perform three basic information processing tasks. 1. Filtering means the extraction of information about a quantity of interest at time t by using data measured up to and including time t. 2. Smoothing differs from filtering in that information about the quantity of interest need not be available at time f, and data measured later than time t can be used in obtaining this information. This means that in the case of smoothing there is a delay in producing the result of interest. Since * The material presented in this chapter is based on the author’s two textbooks: (1) Adaptive Filter Theory (1996) and (2) Neural Networks: A Comprehensive Foundation (1999), Prentice-Hall, Englewood Cliffs, NJ. 0-8493-3691-0/01/$0.00+$.50 © 2001 by CRC Press LLC 2-1
- 47. 2-2 Advanced Signal Processing Handbook in the smoothing process we are able to use data obtained not only up to time t, but also data obtained after time t, we would expect smoothing to be more accurate in some sense than filtering. 3. Prediction is the forecasting side of information processing. The aim here is to derive information about what the quantity of interest will be like at some time t + x in the future, for some x > 0, by using data measured up to and including time t. We may classify filters into linear and nonlinear. A filter is said to be linear if the filtered, smoothed, or predicted quantity at the output of the device is a linearfunction o f the observations applied to the filter input. Otherwise, the filter is nonlinear. In the statistical approach to the solution of the linear filtering problem as classified above, we assume the availability of certain statistical parameters (i.e., mean and correlation functions) of the useful signal and unwanted additive noise, and the requirement is to design a linear filter with the noisy data as input so as to minimize the effects of noise at the filter output according to some statistical criterion. A useful approach to this filter-optimization problem is to minimize the mean-square value of the error signal that is defined as the difference between some desired response and the actual filter output. For stationary inputs, the resulting solution is commonly known as the Wiener filter, which is said to be optimum in the mean-square sense. A plot of the mean-square value of the error signal vs. the adjustable parameters of a linear filter is referred to as the error-performance surface. The minimum point of this surface represents the Wiener solution. The Wiener filter is inadequate for dealing with situations in which nonstationarity of the signal and/or noise is intrinsic to the problem. In such situations, the optimum filter has to assume a time-varying form . A highly successful solution to this more difficult problem is found in the Kalman filter, a powerful device with a wide variety of engineering applications. Linear filter theory, encompassing both Wiener and Kalman filters, has been developed fully in the literature for continuous-time as well as discrete-time signals. However, for technical reasons influenced by the wide availability of digital computers and the ever-increasing use of digital signal-processing devices, we find in practice that the discrete-time representation is often the preferred method. Accordingly, in this chapter, we only consider the discrete-time version of Wiener and Kalman filters. In this method of representation, the input and output signals, as well as the characteristics of the filters themselves, are all defined at discrete instants of time. In any case, a continuous-time signal may always be represented by a sequence o f samples that are derived by observing the signal at uniformly spaced instants of time. No loss of information is incurred during this conversion process provided, of course, we satisfy the well-known sampling theorem, according to which the sampling rate has to be greater than twice the highest frequency component of the continuous-time signal (assumed to be of a low-pass kind). We may thus represent a continuous-time signal u{t) by the sequence u{n), n = 0, ±1, ±2, ..., where for convenience we have normalized the sampling period to unity, a practice that we follow throughout this chapter. 2.2 Adaptive Filters The design of a Wiener filter requires a priori information about the statistics of the data to be processed. The filter is optimum only when the statistical characteristics of the input data match the a priori information on which the design of the filter is based. When this information is not known completely, however, it may not be possible to design the Wiener filter or else the design may no longer be optimum. A straightforward approach that we may use in such situations is the “estimate and plug” procedure. This is a two-stage process whereby the filter first “estimates” the statistical parameters of the relevant signals and then “plugs” the results so obtained into a nonrecursive formula for computing the filter parameters. For a real-time operation, this procedure has the disadvantage of requiring excessively elab orate and costly hardware. A more efficient method is to use an adaptive filter. By such a device we mean one that is self-designing in that the adaptive filter relies on a recursive algorithm for its operation, which makes it possible for the filter to perform satisfactorily in an environment where complete knowledge of
- 48. Adaptive Systems for Signal Process 2-3 the relevant signal characteristics is not available. The algorithm starts from some predetermined set of initial conditions, representing whatever we know about the environment. Yet, in a stationary environ ment, we find that after successive iterations of the algorithm it converges to the optimum Wiener solution in some statistical sense. In a nonstationary environment, the algorithm offers a tracking capability, in that it can track time variations in the statistics of the input data, provided that the variations are sufficiently slow. As a direct consequence of the application of a recursive algorithm whereby the parameters of an adaptive filter are updated from one iteration to the next, the parameters become data dependent. This, therefore, means that an adaptive filter is in reality a nonlinear device, in the sense that it does not obey the principle o f superposition. Notwithstanding this property, adaptive filters are commonly classified as linear or nonlinear. An adaptive filter is said to be linear if the estimate of quantity of interest is computed adaptively (at the output of the filter) as a linear combination o f the available set o f observations applied to the filter input. Otherwise, the adaptive filter is said to be nonlinear. A wide variety of recursive algorithms have been developed in the literature of the operation of linear adaptive filters. In the final analysis, the choice of one algorithm over another is determined by one or more of the following factors: • Rate o f convergence — This is defined as the number of iterations required for the algorithm, in response to stationary inputs, to converge “close enough” to the optimum Wiener solution in the mean-square sense. A fast rate of convergence allows the algorithm to adapt rapidly to a stationary environment of unknown statistics. • Misadjustment — For an algorithm of interest, this parameter provides a quantitative measure of the amount by which the final value of the mean-squared error, averaged over an ensemble of adaptive filters, deviates from the minimum mean-squared error that is produced by the Wiener filter. • Tracking — When an adaptive filtering algorithm operates in a nonstationary environment, the algorithm is required to track statistical variations in the environment. The tracking performance of the algorithm, however, is influenced by two contradictory features: (1) the rate of convergence and (b) the steady-state fluctuation due to algorithm noise. • Robustness — For an adaptive filter to be robust, small disturbances (i.e., disturbances with small energy) can only result in small estimation errors. The disturbances may arise from a variety of factors internal or external to the filter. • Computational requirements — Here, the issues of concern include (1) the number of operations (i.e., multiplications, divisions, and additions/subtractions) required to make one complete iter ation of the algorithm, (2) the size of memory locations required to store the data and the program, and (3) the investment required to program the algorithm on a computer. • Structure — This refers to the structure of information flow in the algorithm, determining the manner in which it is implemented in hardware form. For example, an algorithm whose structure exhibits high modularity, parallelism, or concurrency is well suited for implementation using very large-scale integration (VLSI).* • Numerical properties — When an algorithm is implemented numerically, inaccuracies are produced due to quantization errors. The quantization errors are due to analog-to-digital conversion of the input data and digital representation of internal calculations. Ordinarily, it is the latter source of quantization errors that poses a serious design problem. In particular, there are two basic issues * VLSI technology favors the implementation of algorithms that possess high modularity, parallelism, or concur rency. We say that a structure is modular when it consists of similar stages connected in cascade. By parallelism, we mean a large number of operations being performed side by side. By concurrency, we mean a large number of similar computations being performed at the same time. For a discussion of VLSI implementation of adaptive filters, see Shabhag and Parhi (1994). This book emphasizes the use of pipelining, an architectural technique used for increasing the throughput of an adaptive filtering algorithm.
- 49. 2-4 Advanced Signal Processing Handbook of concern: numerical stability and numerical accuracy. Numerical stability is an inherent charac teristic of an adaptive filtering algorithm. Numerical accuracy, on the other hand, is determined by the number of bits (i.e., binary digits used in the numerical representation of data samples and filter coefficients). An adaptive filtering algorithm is said to be numerically robust when it is insensitive to variations in the word length used in its digital implementation. These factors, in their own ways, also enter into the design of nonlinear adaptive filters, except for the fact that we now no longer have a well-defined frame of reference in the form of a Wiener filter. Rather, we speak of a nonlinear filtering algorithm that may converge to a local minimum or, hopefully, a global minimum on the error-performance surface. In the sections that follow, we shall first discuss various aspects of linear adaptive filters. Discussion of nonlinear adaptive filters is deferred to Section 2.6. 2.3 Linear Filter Structures The operation of a linear adaptive filtering algorithm involves two basic processes: (1) a filtering process designed to produce an output in response to a sequence of input data, and (2) an adaptive process, the purpose of which is to provide mechanism for the adaptive control of an adjustable set of parameters used in the filtering process. These two processes work interactively with each other. Naturally, the choice of a structure for the filtering process has a profound effect on the operation of the algorithm as a whole. There are three types of filter structures that distinguish themselves in the context of an adaptive filter with finite memory or, equivalently, finite-duration impulse response. The three filter structures are trans versal filter, lattice predictor, and systolic array. 2.3.1 Transversal Filter The transversal filter," also referred to as a tapped-delay line filter; consists of three basic elements, as depicted in Figure 2.1: (1) a unit-delay element, (2) a multiplier, and (3) an adder. The number of delay elements used in the filter determines the finite duration of its impulse response. The number of delay elements, shown as M - 1 in Figure 2.1, is commonly referred to as the filter order. In Figure 2.1, the delay elements are each identified by the unit-delay operator z~l. In particular, when z~l operates on the FIGURE 2.1 Transversal filter. * The transversal filter was first described by Kallmann as a continuous-time device whose output is formed as a linear combination of voltages taken from uniformly spaced taps in a nondispersive delay line (Kallmann, 1940). In recent years, the transversal filter has been implemented using digital circuitry, charged-coupled devices, or surface- acoustic wave devices. Owing to its versatility and ease of implementation, the transversal filter has emerged as an essential signal-processing structure in a wide variety of applications.
- 50. Adaptive Systems for Signal Process 2-5 input u(n), the resulting output is u(n - 1). The role of each multiplier in the filter is to multiply the tap input, to which it is connected by a filter coefficient referred to as a tap weight. Thus, a multiplier connected to the fah tap input u(n - k) produces the scalar version of the inner product, wk u(n - k ), where wk is the respective tap weight and k = 0 , 1 , . . M - 1. The asterisk denotes complex conjugation, which assumes that the tap inputs and, therefore, the tap weights are all complex valued. The combined role of the adders in the filter is to sum the individual multiplier outputs and produce an overall filter output. For the transversal filter described in Figure 2.1, the filter output is given by ( 2. 1) Equation 2.1 is called a finite convolution sum in the sense that it convolves the finite-duration impulse response of the filter, w„, with the filter input u(n) to produce the filter output y(n). 2.3.2 Lattice Predictor A lattice predictor is modular in structure in that it consists of a number of individual stages, each of which has the appearance of a lattice, hence, the name “lattice” as a structural descriptor. Figure 2.2 depicts a lattice predictor consisting of M - 1 stages; the number M - 1 is referred to as the predictor order. The mth stage of the lattice predictor in Figure 2.2 is described by the pair of input-output relations (assuming the use of complex-valued, wide-sense stationary input data): ( 2.2) (2.3) where m = 1, 2, ..., M - 1, and M - 1 is the final predictor order. The variable f m(n) is the mth forward prediction error, and bm{n) is the mth backward prediction error. The coefficient Km is called the mth reflection coefficient. The forward prediction error f m(n) is defined as the difference between the input u{n) and its one-step predicted value; the latter is based on the set of m past inputs u(n - 1), ..., u(n - m). Correspondingly, the backward prediction error bm(n) is defined as the difference between the input u(n - m) and its “backward” prediction based on the set of m “future” inputs u(n), ..., u(n - m + 1). Considering the conditions at the input of stage 1 in Figure 2.2, we have (2.4) where u(n) is the lattice predictor input at time n. Thus, starting with the initial conditions of Equation 2.4 and given the set of reflection coefficients kp k2, ..., km_p we may determine the final pair of outputs f M-(n) and bM_ fn ) by moving through the lattice predictor, stage by stage. For a correlated input sequence u(n), u(n - 1), ..., u (n -M -I- 1) drawn from a stationary process, the backward prediction errors b0, b fn ), ..., bM_ fn ) form a sequence of uncorrelated random variables. Moreover, there is a one-to-one correspondence between these two sequences of random variables in the sense that if we are given one of them, we may uniquely determine the other and vice versa. Accordingly, a linear combination of the backward prediction errors b0, b{(n), ..., bM_ fn ) may be used to provide an estimate of some desired response d(n), as depicted in the lower half of Figure 2.2. The arithmetic difference between d{n) and the estimate so produced represents the estimation error e(n). The process described herein is referred to as a joint-process estimation. Naturally, we may use the original input sequence u{n), u(n - 1), ..., u(n - M + 1) to produce an estimate of the desired response d(n) directly. The indirect method depicted in Figure 2.2, however, has the advantage of simplifying the computation * The development of the lattice predictor is credited to Itakura and Saito (1972).
- 51. 2-6 Advanced Signal Processing Handbook FIGURE 2.2 Multistage lattice filter.
- 52. Adaptive Systems for Signal Process 2-7 of the tap weights h0>h ^ n ) , ..., hM_{ by exploiting the uncorrelated nature of the corresponding backward prediction errors used in the estimation. 2.3.3 Systolic Array A systolic array* represents a parallel computing network ideally suited for mapping a number of important linear algebra computations, such as matrix multiplication, triangularization, and back substitution. Two basic types of processing elements may be distinguished in a systolic array: boundary cells and internal cells. Their functions are depicted in Figures 2.3a and 2.3b, respectively. In each case, the parameter r represents a value stored within the cell. The function of the boundary cell is to produce an output equal to the input u divided by the number r stored in the cell. The function of the internal cell is twofold: (1) to multiply the input z (coming in from the top) by the number r stored in the cell, subtract the product rz from the second input (coming in from the left), and thereby produce the difference u - rz as an output from the right-hand side of the cell; and (2) to transmit the first z downward without alteration. FIGURE 2.3 Two basic cells of a systolic array: (a) boundary cell and (b) internal cell. Consider, for example, the 3 x 3 triangular array shown in Figure 2.4. This systolic array involves a combination of boundary and internal cells. In this case, the triangular array computes an output vector y related to the input vector u as follows: (2.5) where the R~Tis the inverse of the transposed matrix RT . The elements of RTare the respective cell contents of the triangular array. The zeros added to the inputs of the array in Figure 2.4 are intended to provide the delays necessary for pipelining the computation described in Equation 2.5. A systolic array architecture, as described herein, offers the desirable features of modularity local interconnections, and highly pipelined and synchronized parallel processing; the synchronization is achieved by means of a global clock. We note that the transversal filter of Figure 2.1, the joint-process estimator of Figure 2.2 based on a lattice predictor, and the triangular systolic array of Figure 2.4 have a common property: all three of * The systolic array was pioneered by Kung and Leiserson (1978). In particular, the use of systolic arrays has made it possible to achieve a high throughput, which is required for many advanced signal-processing algorithms to operate in real time.
- 53. 2-8 Advanced Signal Processing Handbook FIGURE 2.4 Triangular systolic array. them are characterized by an impulse response of finite duration. In other words, they are examples of a finite-duration impulse response (FIR) filter, whose structures contain feedforward paths only. On the other hand, the filter structure shown in Figure 2.5 is an example of an infinite-duration impulse response (HR) filter. The feature that distinguishes an HR filter from an FIR filter is the inclusion o f feedback paths. Indeed, it is the presence of feedback that makes the duration of the impulse response of an HR filter infinitely long. Furthermore, the presence of feedback introduces a new problem, namely, that of stability. In particular, it is possible for an IIR filter to become unstable (i.e., break into oscillation), unless special precaution is taken in the choice of feedback coefficients. By contrast, an FIR filter in inherently stable. This explains the reason for the popular use of FIR filters, in one form or another, as the structural basis for the design of linear adaptive filters. 2.4 Approaches to the Development of Linear Adaptive Filtering Algorithms There is no unique solution to the linear adaptive filtering problem. Rather, we have a “kit of tools” represented by a variety of recursive algorithms, each of which offers desirable features of its own. (For complete detailed treatment of linear adaptive filters, see the book by Haykin [1996].) The challenge facing the user of adaptive filtering is (1) to understand the capabilities and limitations of various adaptive filtering algorithms and (2) to use this understanding in the selection of the appropriate algorithm for the application at hand. Basically, we may identify two distinct approaches for deriving recursive algorithms for the operation of linear adaptive filters, as discussed next.
- 54. Adaptive Systems for Signal Process 2-9 FIGURE 2.5 HR filter. 2.4.1 Stochastic Gradient Approach Here, we may use a tapped-delay line or transversal filter as the structural basis for implementing the linear adaptive filter. For the case of stationary inputs, the costfunction,* also referred to as the index o fperformance, is defined as the mean-squared error (i.e., the mean-square value of the difference between the desired response and the transversal filter output). This cost function is precisely a second-order function of the tap weights in the transversal filter. The dependence of the mean-squared error on the unknown tap weights may be viewed to be in the form of a multidimensional paraboloid (i.e., punch bowl) with a uniquely defined bottom or minimum point. As mentioned previously, we refer to this paraboloid as the error-performance surface; the tap weights corresponding to the minimum point of the surface define the optimum Wiener solution. To develop a recursive algorithm for updating the tap weights of the adaptive transversal filter, we proceed in two stages. We first modify the system of Wiener-Hopf equations (i.e., the matrix equation defining the optimum Wiener solution) through the use of the method o f steepest descent, a well-known technique in ’ In the general definition of a function, we speak of a transformation from a vector space into the space of real (or complex) scalars (Luenberger, 1969; Dorny, 1975). A cost function provides a quantitative measure for assessing the quality of performance and, hence, the restriction of it to a real scalar.
- 55. Exploring the Variety of Random Documents with Different Content
- 56. him: Martin had known all about Burr's criminal enterprise. Jefferson had received a letter from Baltimore stating that this had been believed generally in that city "for more than a twelve-month." Let Hay subpœna as a witness the writer of this letter—one Greybell. Something must be done to "put down" the troublesome "bull- dog": "Shall L M be summoned as a witness against Burr?" Or "shall we move to commit L M as particeps criminis with Burr? Greybell will fix upon him misprision of treason at least ... and add another proof that the most clamorous defenders of Burr are all his accomplices." As for Bollmann! "If [he] finally rejects his pardon, & the Judge decides it to have no effect ... move to commit him immediately for treason or misdemeanor."[1122] But Bollmann, in open court, had refused Jefferson's pardon six days before the President's vindictively emotional letter was written. After Marshall delivered his opinion on the question of the subpœna to Jefferson, Burr insisted, in an argument as convincing as it was brief, that the Chief Justice should now deliver the supplementary charge to the grand jury as to what evidence it could legally consider. Marshall announced that he would do so on the following Monday.[1123] Several witnesses for the Government were sworn, among them Commodore Thomas Truxtun, Commodore Stephen Decatur, and "General" William Eaton. When Dr. Erich Bollmann was called to the book, Hay stopped the administration of the oath. Bollmann had told the Government all about Burr's "plans, designs and views," said the District Attorney; "as these communications might criminate doctor Bollman before the grand jury, the president has communicated to me this pardon"—and Hay held out the shameful document. He had already offered it to Bollmann, he informed Marshall, but that incomprehensible person would neither accept nor reject it. His evidence was "extremely material"; the pardon would "completely exonerate him from all the penalties of the law." And so, exclaimed Hay, "in the presence of this court, I offer this pardon to him, and if
- 57. he refuses, I shall deposit it with the clerk for his use." Then turning to Bollmann, Hay dramatically asked: "Will you accept this pardon?" "No, I will not, sir," firmly answered Bollmann. Then, said Hay, the witness must be sent to the grand jury "with an intimation, that he has been pardoned." "It has always been doctor Bollman's intention to refuse this pardon," broke in Luther Martin. He had not done so before only "because he wished to have this opportunity of publicly rejecting it." Witness after witness was sworn and sent to the grand jury, Hay and Martin quarreling over the effect of Jefferson's pardon of Bollmann. Marshall said that it would be better "to settle ... the validity of the pardon before he was sent to the grand jury." Again Hay offered Bollmann the offensive guarantee of immunity; again it was refused; again Martin protested. "Are you then willing to hear doctor Bollman indicted?" asked Hay, white with anger. "Take care," he theatrically cried to Martin, "in what an awful condition you are placing this gentleman." Bollmann could not be frightened, retorted Martin: "He is a man of too much honour to trust his reputation to the course which you prescribe for him." Marshall "would perceive," volunteered the nonplussed and exasperated Hay, "that doctor Bollman now possessed so much zeal, as even to encounter the risk of an indictment for treason." The Chief Justice announced that he could not, "at present, declare, whether he be really pardoned or not." He must, he said, "take time to deliberate." Hay persisted: "Categorically then I ask you, Mr. Bollman, do you accept your pardon?"
- 58. "I have already answered that question several times. I say no," responded Bollmann. "I repeat, that I would have refused it before, but that I wished this opportunity of publicly declaring it."[1124] Bollmann was represented by an attorney of his own, a Mr. Williams, who now cited an immense array of authorities on the various questions involved. Counsel on both sides entered into the discussion. One "reason why doctor Bollman has refused this pardon" was, said Martin, "that it would be considered as an admission of guilt." But "doctor Bollman does not admit that he has been guilty. He does not consider a pardon as necessary for an innocent man. Doctor Bollman, sir, knows what he has to fear from the persecution of an angry government; but he will brave it all." Yes! cried Martin, with immense effect on the excited spectators, "the man, who did so much to rescue the marquis la Fayette from his imprisonment, and who has been known at so many courts, bears too great a regard for his reputation, to wish to have it sounded throughout Europe, that he was compelled to abandon his honour through a fear of unjust persecution." Finally the true- hearted and defiant Bollmann was sent to the grand jury without having accepted the pardon, and without the legal effect of its offer having been decided.[1125] When the Richmond Enquirer, containing Marshall's opinion on the issuance of the subpœna duces tecum, reached Washington, the President wrote to Hay an answer of great ability, in which Jefferson the lawyer shines brilliantly forth: "As is usual where an opinion is to be supported, right or wrong, he [Marshall] dwells much on smaller objections, and passes over those which are solid.... He admits no exception" to the rule "that all persons owe obedience to subpœnas ... unless it can be produced in his law books." "But," argues Jefferson, "if the Constitution enjoins on a particular officer to be always engaged in a particular set of duties imposed on him, does not this supersede the general law, subjecting him to minor duties inconsistent with these? The Constitution enjoins his
- 59. [the President's] constant agency in the concerns of 6. millions of people. Is the law paramount to this, which calls on him on behalf of a single one?" Let Marshall smoke his own tobacco: suppose the Sheriff of Henrico County should summon the Chief Justice to help "quell a riot"? Under the "general law" he is "a part of the posse of the State sheriff"; yet, "would the Judge abandon major duties to perform lesser ones?" Or, imagine that a court in the most distant territory of the United States "commands, by subpœnas, the attendance of all the judges of the Supreme Court. Would they abandon their posts as judges, and the interests of millions committed to them, to serve the purposes of a single individual?" The Judiciary was incessantly proclaiming its "independence," and asserting that "the leading principle of our Constitution is the independence of the Legislature, executive and judiciary of each other." But where would be such independence, if the President "were subject to the commands of the latter, & to imprisonment for disobedience; if the several courts could bandy him from pillar to post, keep him constantly trudging from north to south & east to west, and withdraw him entirely from his constitutional duties?" Jefferson vigorously resented Marshall's personal reference to him. "If he alludes to our annual retirement from the seat of government, during the sickly season," Hay ought to tell Marshall that Jefferson carried on his Executive duties at Monticello.[1126] Crowded with sensations as the proceedings had been from the first, they now reached a stage of thrilling movement and high color. The long-awaited and much-discussed Wilkinson had at last arrived "with ten witnesses, eight of them Burr's select men," as Hay gleefully reported to Jefferson.[1127] Fully attired in the showy uniform of the period, to the last item of martial decoration, the fat, pompous Commanding General of the American armies strode through the crowded streets of Richmond and made his way among
- 60. the awed and gaping throng to his seat by the side of the Government's attorneys. Washington Irving reports that "Wilkinson strutted into the Court, and ... stood for a moment swelling like a turkey cock." Burr ignored him until Marshall "directed the clerk to swear General Wilkinson; at the mention of the name Burr turned his head, looked him full in the face with one of his piercing regards, swept his eye over his whole person from head to foot, as if to scan its dimensions, and then coolly ... went on conversing with his counsel as tranquilly as ever." [1128] Wilkinson delighted Jefferson with a different description: "I saluted the Bench & in spite of myself my Eyes darted a flash of indignation at the little Traitor, on whom they continued fixed until I was called to the Book—here Sir I found my expectations verified— This Lyon hearted Eagle Eyed Hero, sinking under the weight of conscious guilt, with haggard Eye, made an Effort to meet the indignant salutation of outraged Honor, but it was in vain, his audacity failed Him, He averted his face, grew pale & affected passion to conceal his perturbation."[1129] But the countenance of a thin, long-faced, roughly garbed man sitting among the waiting witnesses was not composed when Wilkinson appeared. For three weeks Andrew Jackson to all whom he met had been expressing his opinion of Wilkinson in the unrestrained language of the fighting frontiersman;[1130] and he now fiercely gazed upon the creature whom he regarded as a triple traitor, his own face furious with scorn and loathing. Within the bar also sat that brave and noble man whose career of unbroken victories had made the most brilliant and honorable page thus far in the record of the American Navy—Commodore Thomas Truxtun. He was dressed in civilian attire.[1131] By his side, clad as a man of business, sat a brother naval hero of the old days, Commodore Stephen Decatur.[1132] A third of the group was
- 61. Benjamin Stoddert, the Secretary of the Navy under President Adams.[1133] In striking contrast with the dignified appearance and modest deportment of these gray-haired friends was the gaudily appareled, aggressive mannered Eaton, his restlessness and his complexion advertising those excesses which were already disgusting even the hard-drinking men then gathered in Richmond. Dozens of inconspicuous witnesses found humbler places in the audience, among them Sergeant Jacob Dunbaugh, bearing himself with mingled bravado, insolence, and humility, the stripes on the sleeve of his uniform designating the position to which Wilkinson had restored him. Dunbaugh had gone before the grand jury on Saturday, as had Bollmann; and now, one by one, Truxtun, Decatur, Eaton, and others were sent to testify before that body. Eaton told the grand jury the same tale related in his now famous affidavit.[1134] Commodore Truxtun testified to facts as different from the statements made by "the hero of Derne"[1135] as though Burr had been two utterly contrasted persons. During the same period that Burr had seen Eaton, he had also conversed with him, said Truxtun. Burr mentioned a great Western land speculation, the digging of a canal, and the building of a bridge. Later on Burr had told him that "in the event of a war with Spain, which he thought inevitable, ... he contemplated an expedition to Mexico," and had asked Truxtun "if the Havanna could be easily taken ... and what would be the best mode of attacking Carthagena and La Vera Cruz by land and sea." The Commodore had given Burr his opinion "very freely," part of it being that "it would require a naval force." Burr had answered that "that might be obtained," and had frankly asked Truxtun if he "would take the command of a naval expedition."
- 62. "I asked him," testified Truxtun, "if the executive of the United States were privy to, or concerned in the project? He answered emphatically that he was not: ... I told Mr. Burr that I would have nothing to do with it.... He observed to me, that in the event of a war [with Spain], he intended to establish an independent government in Mexico; that Wilkinson, the army, and many officers of the navy would join.... Wilkinson had projected the expedition, and he had matured it; that many greater men than Wilkinson would join, and that thousands to the westward would join." In some of the conversations "Burr mentioned to me that the government was weak," testified Truxtun, "and he wished me to get the navy of the United States out of my head;[1136] ... and not to think more of those men at Washington; that he wished to see or make me, (I do not recollect which of those two terms he used) an Admiral." Burr wished Truxtun to write to Wilkinson, to whom he was about to dispatch couriers, but Truxtun declined, as he "had no subject to write about." Again Burr urged Truxtun to join the enterprise —"several officers would be pleased at being put under my command.... The expedition could not fail—the Mexicans were ripe for revolt." Burr "was sanguine there would be war," but "if he was disappointed as to the event of war, he was about to complete a contract for a large quantity of land on the Washita; that he intended to invite his friends to settle it; that in one year he would have a thousand families of respectable and fashionable people, and some of them of considerable property; that it was a fine country, and that they would have a charming society, and in two years he would have doubled the number of settlers; and being on the frontier, he would be ready to move whenever a war took place.... "All his conversations respecting military and naval subjects, and the Mexican expedition, were in the event of a war with Spain." Truxtun testified that he and Burr were "very intimate"; that Burr
- 63. talked to him with "no reserve"; and that he "never heard [Burr] speak of a division of the union." Burr had shown Truxtun the plan of a "kind of boat that plies between Paulus-Hook and New-York," and had asked whether such craft would do for the Mississippi River and its tributaries, especially on voyages upstream. Truxtun had said they would. Burr had asked him to give the plans to "a naval constructor to make several copies," and Truxtun had done so. Burr explained that "he intended those boats for the conveyance of agricultural products to market at New-Orleans, and in the event of war [with Spain], for transports." The Commodore testified that Burr made no proposition to invade Mexico "whether there was war [with Spain] or not." He was so sure that Burr meant to settle the Washita lands that he was "astonished" at the newspaper accounts of Burr's treasonable designs after he had gone to the Western country for the second time. Truxtun had freely complained of what amounted to his discharge from the Navy, being "pretty full" himself of "resentment against the Government," and Burr "joined [him] in opinion" on the Administration.[1137] Jacob Dunbaugh told a weird tale. At Fort Massac he had been under Captain Bissel and in touch with Burr. His superior officer had granted him a furlough to accompany Burr for twenty days. Before leaving, Captain Bissel had "sent for [Dunbaugh] to his quarters," told him to keep "any secrets" Burr had confided to him, and "advised" him "never to forsake Col. Burr"; and "at the same time he made [Dunbaugh] a present of a silver breast plate." After Dunbaugh had joined the expedition, Burr had tried to persuade him to get "ten or twelve of the best men" among his nineteen fellow soldiers then at Chickasaw Bluffs to desert and join the expedition; but the virtuous sergeant had refused. Then Burr had asked him to "steal from the garrison arms such as muskets, fusees and rifles," but Dunbaugh had also declined this reasonable
- 64. request. As soon as Burr learned of Wilkinson's action, he told Dunbaugh to come ashore with him armed "with a rifle," and to "conceal a bayonet under [his] clothes.... He told me he was going to tell me something I must never relate again, ... that General Wilkinson had betrayed him ... that he had played the devil with him, and had proved the greatest traitor on the earth." Just before the militia broke up the expedition, Burr and Wylie, his secretary, got "an axe, auger and saw," and "went into Colonel Burr's private room and began to chop," Burr first having "ordered no person to go out." Dunbaugh did go out, however, and "got on the top of the boat." When the chopping ceased, he saw that "a Mr. Pryor and a Mr. Tooly got out of the window," and "saw two bundles of arms tied up with cords, and sunk by cords going through the holes at the gunwales of Colonel Burr's boat." The vigilant Dunbaugh also saw "about forty or forty-three stands [of arms], besides pistols, swords, blunderbusses, fusees, and tomahawks"; and there were bayonets too.[1138] Next Wilkinson detailed to the grand jury the revelations he had made to Jefferson. He produced Burr's cipher letter to him, and was forced to admit that he had left out the opening sentence of it —"Yours, postmarked 13th of May, is received"—and that he had erased some words of it and substituted others. He recounted the alarming disclosures he had so cunningly extracted from Burr's messenger, and enlarged upon the heroic measures he had taken to crush treason and capture traitors. For four days[1139] Wilkinson held forth, and himself escaped indictment by the narrow margin of 7 to 9 of the sixteen grand jurymen. All the jurymen, however, appear to have believed him to be a scoundrel.[1140] "The mammoth of iniquity escaped," wrote John Randolph in acrid disgust, "not that any man pretended to think him innocent, but upon certain wire-drawn distinctions that I will not pester you with. Wilkinson is the only man I ever saw who was from the bark to the very core a villain.... Perhaps you never saw human nature in so
- 65. degraded a situation as in the person of Wilkinson before the grand jury, and yet this man stands on the very summit and pinnacle of executive favor."[1141] Samuel Swartwout, the courier who had delivered Burr's ill-fated letter, "most positively denied" that he had made the revelations which Wilkinson claimed to have drawn from him.[1142] The youthful Swartwout as deeply impressed the grand jury with his honesty and truthfulness as Wilkinson impressed that body with his untrustworthiness and duplicity.[1143] Peter Taylor and Jacob Allbright then recounted their experiences. [1144] And the Morgans told of Burr's visit and of their inferences from his mysterious tones of voice, glances of eye, and cryptic expressions. So it was, that in spite of overwhelming testimony of other witnesses,[1145] who swore that Burr's purposes were to settle the Washita lands and in the event of war with Spain, and only in that event, to invade Mexico, with never an intimation of any project hostile to the United States—so it was that bills of indictment for treason and for misdemeanor were, on June 24, found against Aaron Burr of New York and Harman Blennerhassett of Virginia. The indictment for treason charged that on December 13, 1806, at Blennerhassett's island in Virginia, they had levied war on the United States; and the one for misdemeanor alleged that, at the same time and place, they had set on foot an armed expedition against territory belonging to His Catholic Majesty, Charles IV of Spain.[1146] This result of the grand jury's investigations was reached because of that body's misunderstanding of Marshall's charge and of his opinion in the Bollmann and Swartwout case.[1147] John Randolph, as foreman of the grand jury, his nose close to the ground on the scent of the principal culprit, came into court the day after the indictment of Burr and Blennerhassett and asked for the letter from Wilkinson to Burr, referred to in Burr's cipher dispatch to Wilkinson, and now in the possession of the accused. Randolph said
- 66. that, of course, the grand jury could not ask Burr to appear before them as a witness, but that they did want the letter. Marshall declared "that the grand jury were perfectly right in the opinion." Burr said that he could not reveal a confidential communication, unless "the extremity of circumstances might impel him to such a conduct." He could not, for the moment, decide; but that "unless it were extorted from him by law" he could not even "deliberate on the proposition to deliver up any thing which had been confided to his honour." Marshall announced that there was no "objection to the grand jury calling before them and examining any man ... who laid under an indictment." Martin agreed "there could be no objection." The grand jury did not want Burr as a witness, said John Randolph. They asked only for the letter. If they should wish Burr's presence at all, it would be only for the purpose of identifying it. So the grand jury withdrew.[1148] Hay was swift to tell his superior all about it, although he trembled between gratification and alarm. "If every trial were to be like that, I am doubtful whether my patience will sustain me while I am wading thro' this abyss of human depravity." Dutifully he informed the President that he feared that "the Gr: Jury had not dismissed all their suspicions of Wilkinson," for John Randolph had asked for his cipher letter to Burr. Then he described to Jefferson the intolerable prisoner's conduct: "Burr rose immediately, & declared that no consideration, no calamity, no desperation, should induce him to betray a letter confidentially written. He could not even allow himself to deliberate on a point, where his conduct was prescribed by the clearest principles of honor &c. &c. &c." Hay then related what Marshall and John Randolph had said, underscoring the statement that "the Gr: Jury did not want A. B. as a witness." Hay did full credit, however, to Burr's appearance of
- 67. candor: "The attitude & tone assumed by Burr struck everybody. There was an appearance of honor and magnanimity which brightened the countenances of the phalanx who daily attend, for his encouragement & support."[1149] Day after day was consumed in argument on points of evidence, while the grand jury were examining witnesses. Marshall delivered a long written opinion upon the question as to whether a witness could be forced to give testimony which he believed might criminate himself. The District Attorney read Jefferson's two letters upon the subject of the subpœna duces tecum. No pretext was too fragile to be seized by one side or the other, as the occasion for argument upon it demanded—for instance, whether or not the District Attorney might send interrogatories to the grand jury. Always the lawyers spoke to the crowd as well as to the court, and their passages at arms became ever sharper.[1150] Wilkinson is "an honest man and a patriot"—no! he is a liar and a thief; Louisiana is a "poor, unfortunate, enslaved country"; letters had been seized by "foulness and violence"; the arguments of Burr's attorneys are "mere declamations"; the Government's agents are striving to prevent Burr from having "a fair trial ... the newspapers and party writers are employed to cry and write him down; his counsel are denounced for daring to defend him; the passions of the grand jury are endeavored to be excited against him, at all events"; [1151] Hay's mind is "harder than Ajax's seven fold shield of bull's hide"; Edmund Randolph came into court "with mysterious looks of awe and terror ... as if he had something to communicate which was too horrible to be told"; Hay is always "on his heroics"; he "hopped up like a parched pea"; the object of Burr's counsel is "to prejudice the surrounding multitude against General Wilkinson"; one newspaper tale is "as impudent a falsehood as ever malignity had uttered"—such was the language with which the arguments were adorned. They were, however, well sprinkled with citations of authority.[1152]
- 68. FOOTNOTES: [1017] See vol. i, 201, of this work. [1018] Tobacco chewing and smoking in court-rooms continued in most American communities in the South and West down to a very recent period. [1019] Address of John Tyler on "Richmond and its Memories," Tyler, i, 219. [1020] Irving was twenty-four years old when he reported the Burr trial. [1021] Blennerhassett Papers: Safford, 465. Marshall made this avowal to Luther Martin, who personally told Blennerhassett of it. [1022] Judge Francis M. Finch, in Dillon, i, 402. "The men who framed that instrument [Constitution] remembered the crimes that had been perpetrated under the pretence of justice; for the most part they had been traitors themselves, and having risked their necks under the law they feared despotism and arbitrary power more than they feared treason." (Adams: U.S. iii, 468.) [1023] A favorite order from the bench for the execution of the condemned was that the culprit should be drawn prostrate at the tails of horses through the jagged and filthy streets from the court-room to the place of execution; the legs, arms, nose, and ears there cut off; the intestines ripped out and burned "before the eyes" of the victim; and finally the head cut off. Details still more shocking were frequently added. See sentences upon William, Lord Russell, July 14, 1683 (State Trials Richard II to George I, vol. 3, 660); upon Algernon Sidney, November 26, 1683 (ib. 738); upon William, Viscount Stafford, December 7, 1680 (ib. 214); upon William Stayley, November 21, 1678 (ib. vol. 2, 656); and upon other men condemned for treason. [1024] Even in Philadelphia, after the British evacuation of that place during the Revolution, hundreds were tried for treason.
- 69. Lewis alone, although then a very young lawyer, defended one hundred and fifty-two persons. (See Chase Trial, 21.) [1025] "In the English law ... the rule ... had been that enough heads must be cut off to glut the vengeance of the Crown." (Isaac N. Phillips, in Dillon, ii, 394.) [1026] Iredell's charge to the Georgia Grand Jury, April 26, 1792, Iredell: McRee, ii, 349; and see Iredell's charge to the Massachusetts Grand Jury, Oct. 12, 1792, ib. 365. [1027] See his concurrence with Judge Peters's charge in the Fries case, Wharton: State Trials, 587-91; and Peters's opinion, ib. 586; also see Chase's charge at the second trial of Fries, ib. 636. [1028] "The President's popularity is unbounded, and his will is that of the nation.... Such is our present infatuation." (Nicholson to Randolph, April 12, 1807, Adams: Randolph, 216-17.) [1029] Hildreth, iv, 692. [1030] Parton: Burr, 458. [1031] Parton: Jackson, i, 333. [1032] Jackson to Anderson, June 16, 1807, ib. 334. [1033] Ib. 335. [1034] Ib. 334-36. [1035] Parton: Burr, 606-08; see also Parton: Jackson, ii, 258- 59, 351-54; and Davis, ii, 433-36. [1036] Address of John Tyler, "Richmond and its Memories," Tyler, i, 219. [1037] Parton: Burr, 459. [1038] Memoirs of Lieut.-General Scott, i, 13. [1039] Memoirs of Lieut.-General Scott, i, 13, 16. [1040] See Great American Lawyers: Lewis, ii, 268-75.
- 70. Kennedy says that the stories of Wirt's habits of intoxication were often exaggerated (Kennedy, i, 68); but see his description of the bar of that period and his apologetic reference to Wirt's conviviality (ib. 66-67). [1041] Blennerhassett Papers: Safford, 426. [1042] Parton: Burr, 461. [1043] Burr Trials, i, 31-32. [1044] Ib. 37. [1045] Ib. 38. [1046] Meaning the partiality of the persons challenged, such as animosity toward the accused, conduct showing bias against him, and the like. See Bouvier's Law Dictionary: Rawle, 3d revision, ii, 1191. [1047] Burr Trials, i, 38-39. [1048] Ib. 41-42. [1049] Burr Trials, i, 41-42. [1050] Jefferson to Nicholas, Feb. 28, 1807, Works: Ford, x, 370-71. [1051] Burr Trials, i, 43. [1052] Ib. 44. [1053] In view of the hatred which Marshall knew Randolph felt toward Jefferson, it is hard to reconcile his appointment with the fairness which Marshall tried so hard to display throughout the trial. However, several of Jefferson's most earnest personal friends were on the grand jury, and some of them were very powerful men. Also fourteen of the grand jury were Republicans and only two were Federalists. [1054] Burr Trials, i, 45-46. This grand jury included some of the foremost citizens of Virginia. The sixteen men who composed this body were: John Randolph, Jr., Joseph Eggleston, Joseph C. Cabell, Littleton W. Tazewell, Robert Taylor, James Pleasants, John
- 71. Brockenbrough, William Daniel, James M. Garnett, John Mercer, Edward Pegram, Munford Beverly, John Ambler, Thomas Harrison, Alexander Shephard, and James Barbour. [1055] Marshall's error in this opinion, or perhaps the misunderstanding of a certain passage of it (see supra, 350), caused him infinite perplexity during the trial; and he was put to his utmost ingenuity to extricate himself. The misconstruction by the grand jury of the true meaning of Marshall's charge was one determining cause of the grand jury's decision to indict Burr. (See infra, 466.) [1056] Burr Trials, i, 47-48. [1057] Hay to Jefferson, May 25, 1807, Jefferson MSS. Lib. Cong. [1058] Burr Trials, i, 48-51. [1059] Burr Trials, i, 53-54. [1060] Irving to Paulding, June 22, 1807, Life and Letters of Washington Irving: Irving, i, 145. [1061] Burr Trials, i, 57-58. [1062] Burr Trials, i, 58-76. [1063] "I ... contented myself ... with ... declaring to the Audience (for two thirds of our speeches have been addressed to the people) that I was prepared to give the most direct contradiction to the injurious Statements." (Hay to Jefferson, June 14, 1807, giving the President an account of the trial, Jefferson MSS. Lib. Cong.) [1064] He was hanged in effigy soon after the trial. (See infra, 539.) [1065] It must be remembered that Marshall himself declared, in the very midst of the contest, that it would be dangerous for a jury to acquit Burr. (See supra, 401.) [1066] He had narrowly escaped impeachment (see supra, chap. iv), and during the trial he was openly threatened with that ordeal (see infra, 500).
- 72. [1067] Burr Trials, i, 79-81. [1068] See supra, 390-91. [1069] Jefferson to Hay, May 26, 1807, Works: Ford, x, footnote to 394-95. [1070] Burr Trials, i, 81-82. [1071] Ib. 82. [1072] Ib. 84-85. [1073] Burr Trials, i, 91. [1074] Ib. 94. [1075] Ib. 95-96. [1076] Burr Trials, i, 492-97. [1077] Burr Trials, i, 509-14. [1078] Burr Trials, i, 97-101. [1079] Ib. 97. [1080] Md. Hist. Soc. Fund-Pub. No. 24, 22. [1081] Blennerhassett Papers: Safford, 468-69. [1082] Burr Trials, i, 101-04. [1083] Burr Trials, i, 105. [1084] The men who went on this second bail bond for Burr were: William Langburn, Thomas Taylor, John G. Gamble, and Luther Martin. (Ib. 106.) [1085] Blennerhassett Papers: Safford, 315-16. [1086] Eaton: Prentiss, 396-403; 4 Cranch, 463-66. [1087] Blennerhassett Papers: Safford, 425. [1088] Jefferson to Hay, May 28, 1807, Works: Ford, x, 395-96.
- 73. [1089] Jefferson to Eppes, May 28, 1807, Works: Ford, x, 412- 13. [1090] Hay to Jefferson, May 31, 1807, Jefferson MSS. Lib. Cong. [1091] Jefferson to Hay, June 2, 1807, Works: Ford, x, 396-97. [1092] Same to same, June 5, 1807, ib. 397-98; Hay to Jefferson, same date, Jefferson MSS. Lib. Cong.; and others cited, infra. [1093] Jefferson to Dayton, Aug. 17, 1807, Works: Ford, x, 478. [1094] Irving to Mrs. Hoffman, June 4, 1807, Irving, i, 142. [1095] Ib. [1096] Burr had seen the order in the Natchez Gazette. It was widely published. [1097] Burr Trials, i, 113-14. [1098] Burr Trials, i, 115-18. [1099] Hay to Jefferson, June 9, 1807, Jefferson MSS. Lib. Cong. [1100] Jefferson to Hay, June 12, 1807, Works: Ford, x, 398-99. [1101] Burr Trials, i, 124-25. [1102] Irving to Mrs. Hoffman, June 4, 1807, Irving, i, 143. [1103] Martin here refers to what he branded as "the farcical trials of Ogden and Smith." In June and July, 1806, William S. Smith and Samuel G. Ogden of New York were tried in the United States Court for that district upon indictments charging them with having aided Miranda in his attack on Caracas, Venezuela. They made affidavit that the testimony of James Madison, Secretary of State, Henry Dearborn, Secretary of War, Robert Smith, Secretary of the Navy, and three clerks of the State Department, was necessary to their defense. Accordingly these officials were summoned to appear in court. They refused, but on July 8, 1806, wrote to the Judges—William Paterson of the Supreme Court and
- 74. Matthias B. Talmadge, District Judge—that the President "has specially signified to us that our official duties cannot ... be at this juncture dispensed with." (Trials of Smith and Ogden: Lloyd, stenographer, 6-7.) The motion for an attachment to bring the secretaries and their clerks into court was argued for three days. The court disagreed, and no action therefore was taken. (Ib. 7-90.) One judge (undoubtedly Paterson) was "of opinion, that the absent witnesses should be laid under a rule to show cause, why an attachment should not be issued against them"; the other (Talmadge) held "that neither an attachment in the first instance, nor a rule to show cause ought to be granted." (Ib. 89.) Talmadge was a Republican, appointed by Jefferson, and charged heavily against the defendants (ib. 236-42, 287); but they were acquitted. The case was regarded as a political prosecution, and the refusal of Cabinet officers and department clerks to obey the summons of the court, together with Judge Talmadge's disagreement with Justice Paterson—who in disgust immediately left the bench under plea of ill-health (ib. 90)—and the subsequent conduct of the trial judge, were commented upon unfavorably. These facts led to Martin's reference during the Burr trial. [1104] Burr Trials, i, 127-28. [1105] Burr Trials, i, 130-33. [1106] Ib. 134-35. [1107] Burr Trials, i, 137-45. [1108] Burr Trials, i, 147-48. [1109] Ib. 148-52. [1110] Burr Trials, i, 153-64. [1111] Burr Trials, i, 164-67. [1112] Ib. 173-76.
- 75. [1113] Burr Trials, i, 177. [1114] See infra, 455-56. [1115] Burr Trials, i, 181-83. [1116] United States vs. Smith and Ogden. (See supra, 436, foot-note.) [1117] Burr Trials, i, 187-88. [1118] Burr Trials, i, 189. [1119] Hay to Jefferson, June 14, 1807, Jefferson MSS. Lib. Cong. [1120] Ambler: Thomas Ritchie—A Study in Virginia Politics, 40- 41. [1121] Jefferson to Hay, June 17, 1807, Works: Ford, x, 400-01. [1122] Jefferson to Hay, June 19, 1807, Works: Ford, x, 402-03. [1123] Burr Trials, i, 190. [1124] Burr Trials, i, 191-93. [1125] Burr Trials, i, 193-96. [1126] Jefferson to Hay, June 20, 1807, Works: Ford, x, 403-05. [1127] Hay to Jefferson, June 11, 1807, Jefferson MSS. Lib. Cong. This letter announced Wilkinson's landing at Hampton Roads. Wilkinson reached Richmond by stage on Saturday, June 13. He was accompanied by John Graham and Captain Gaines, the ordinary witnesses having been sent ahead on a pilot boat. (Graham to Madison, May 11, 1807, "Letters in Relation," MSS. Lib. Cong.) Graham incorrectly dated his letter May 11 instead of June 11. He had left New Orleans in May, and in the excitement of landing had evidently forgotten that a new month had come. Wilkinson was "too much fatigued" to come into court. (Burr Trials, i, 196.) By Monday, however, he was sufficiently restored to present himself before Marshall.
- 76. [1128] Irving to Paulding, June 22, 1807, Irving, i, 145. [1129] Wilkinson to Jefferson, June 17, 1807, "Letters in Relation," MSS. Lib. Cong. The court reporter impartially states that Wilkinson was "calm, dignified, and commanding," and that Burr glanced at him with "haughty contempt." (Burr Trials, i, footnote to 197.) [1130] "Gen: Jackson of Tennessee has been here ever since the 22ḍ [of May] denouncing Wilkinson in the coarsest terms in every company." (Hay to Jefferson, June 14, 1807, Jefferson MSS. Lib. Cong.) Hay had not the courage to tell the President that Jackson had been as savagely unsparing in his attacks on Jefferson as in his thoroughly justified condemnation of Wilkinson. [1131] Truxtun left the Navy in 1802, and, at the time of the Burr trial, was living on a farm in New Jersey. No officer in any navy ever made a better record for gallantry, seamanship, and whole-hearted devotion to his country. The list of his successful engagements is amazing. He was as high-spirited as he was fearless and honorable. In 1802, when in command of the squadron that was being equipped for our war with Tripoli, Truxtun most properly asked that a captain be appointed to command the flagship. The Navy was in great disfavor with Jefferson and the whole Republican Party, and naval affairs were sadly mismanaged or neglected. Truxtun's reasonable request was refused by the Administration, and he wrote a letter of indignant protest to the Secretary of the Navy. To the surprise and dismay of the experienced and competent officer, Jefferson and his Cabinet construed his spirited letter as a resignation from the service, and, against Truxtun's wishes, accepted it as such. Thus the American Navy lost one of its ablest officers at the very height of his powers. Truxtun at the time was fifty-two years old. No single act of Jefferson's Administration is more discreditable than this untimely ending of a great career. [1132] This man was the elder Decatur, father of the more famous officer of the same name. He had had a career in the American Navy as honorable but not so distinguished as that of
- 77. Truxtun; and his service had been ended by an unhappy circumstance, but one less humiliating than that which severed Truxtun's connection with the Navy. The unworthiest act of the expiring Federalist Congress of 1801, and one which all Republicans eagerly supported, was that authorizing most of the ships of the Navy to be sold or laid up and most of the naval officers discharged. (Act of March 3, 1801, Annals, 6th Cong. 1st and 2d Sess. 1557-59.) Among the men whose life profession was thus cut off, and whose notable services to their country were thus rewarded, was Commodore Stephen Decatur, who thereafter engaged in business in Philadelphia. [1133] It was under Stoddert's administration of the Navy Department that the American Navy was really created. Both Truxtun and Decatur won their greatest sea battles in our naval war with France, while Stoddert was Secretary. The three men were close friends and all of them warmly resented the demolition of the Navy and highly disapproved of Jefferson, both as an individual and as a statesman. They belonged to the old school of Federalists. Three more upright men did not live. [1134] See supra, 304-05. [1135] A popular designation of Eaton after his picturesque and heroic Moroccan exploit. [1136] Truxtun at the time of his conversations with Burr was in the thick of that despair over his cruel and unjustifiable separation from the Navy, which clouded his whole after life. The longing to be once more on the quarter-deck of an American warship never left his heart. [1137] Burr Trials, i, 486-91. This abstract is from the testimony given by Commodore Truxtun before the trial jury, which was substantially the same as that before the grand jury. [1138] Annals, 10th Cong. 1st Sess. 452-63. See note 1, next page. [1139] Wilkinson's testimony on the trial for misdemeanor (Annals, 10th Cong. 1st Sess, 520-22) was the same as before the grand jury.
- 78. "Wilkinson is now before the grand jury, and has such a mighty mass of words to deliver himself of, that he claims at least two days more to discharge the wondrous cargo." (Irving to Paulding, June 22, 1807, Irving, i, 145.) [1140] See McCaleb, 335. Politics alone saved Wilkinson. The trial was universally considered a party matter, Jefferson's prestige, especially, being at stake. Yet seven out of the sixteen members of the grand jury voted to indict Wilkinson. Fourteen of the jury were Republicans, and two were Federalists. [1141] Randolph to Nicholson, June 25, 1807, Adams: Randolph, 221-22. Speaking of political conditions at that time, Randolph observed: "Politics have usurped the place of law, and the scenes of 1798 [referring to the Alien and Sedition laws] are again revived." [1142] Testimony of Joseph C. Cabell, one of the grand jury. (Annals, 10th Cong. 1st Sess. 677.) [1143] "Mr. Swartwout ... discovered the utmost frankness and candor in his evidence.... The very frank and candid manner in which he gave his testimony, I must confess, raised him very high in my estimation, and induced me to form a very different opinion of him from that which I had before entertained." (Testimony of Littleton W. Tazewell, one of the grand jury, Annals, 10th Cong. 1st Sess. 633.) "The manner of Mr. Swartwout was certainly that of conscious innocence." (Testimony of Joseph C. Cabell, one of the grand jury, ib. 677.) [1144] See supra, 426-27. [1145] Forty-eight witnesses were examined by the grand jury. The names are given in Brady: Trial of Aaron Burr, 69-70. [1146] Burr Trials, i, 305-06; also "Bills of Indictment," MSS. Archives of the United States Court, Richmond, Va. The following day former Senator Jonathan Dayton of New Jersey, Senator John Smith of Ohio, Comfort Tyler and Israel Smith of New York, and Davis Floyd of the Territory of Indiana, were presented for treason. How Bollmann, Swartwout, Adair, Brown, and others escaped indictment is only less
- 79. comprehensible than the presentment of Tyler, Floyd, and the two Smiths for treason. [1147] Blennerhassett Papers: Safford, 314. "Two of the most respectable and influential of that body, since it has been discharged, have declared they mistook the meaning of Chief Justice Marshall's opinion as to what sort of acts amounted to treason in this country, in the case of Swartwout and Ogden [Bollmann]; that it was under the influence of this mistake they concurred in finding such a bill against A. Burr, which otherwise would have probably been ignored." [1148] Burr Trials, i, 327-28. [1149] Hay to Jefferson, June 25, 1807, Jefferson MSS. Lib. Cong. [1150] Burr Trials, i, 197-357. [1151] This was one of Luther Martin's characteristic outbursts. Every word of it, however, was true. [1152] Burr Trials, i, 197-357.
- 80. CHAPTER IX WHAT IS TREASON? No person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court. (Constitution, Article III, Section 3.) Such are the jealous provisions of our laws in favor of the accused that I question if he can be convicted. (Jefferson.) The scenes which have passed and those about to be transacted will hereafter be deemed fables, unless attested by very high authority. (Aaron Burr.) That this court dares not usurp power is most true. That this court dares not shrink from its duty is no less true. (Marshall.) While the grand jury had been examining witnesses, interesting things had taken place in Richmond. Burr's friends increased in number and devotion. Many of them accompanied him to and from court each day.[1153] Dinners were given in his honor, and Burr returned these courtesies, sometimes entertaining at his board a score of men and women of the leading families of the city.[1154] Fashionable Richmond was rapidly becoming Burr-partisan. In society, as at the bar, the Government had been maneuvered into defense. Throughout the country, indeed, Burr's numerous adherents had proved stanchly loyal to him. "I believe," notes Senator Plumer in his diary, "even at this period, that no man in this country, has more personal friends or who are more firmly attached to his interests—or would make greater sacrifices to aid him than this man."[1155] But this availed Burr nothing as against the opinion of the multitude, which Jefferson manipulated as he chose. Indeed, save in Richmond, this very
- 81. fidelity of Burr's friends served rather to increase the public animosity; for many of these friends were persons of standing, and this fact did not appeal favorably to the rank and file of the rampant democracy of the period. In Richmond, however, Burr's presence and visible peril animated his followers to aggressive action. On the streets, in the taverns and drinking-places, his adherents grew bolder. Young Swartwout chanced to meet the bulky, epauletted Wilkinson on the sidewalk. Flying into "a paroxysm of disgust and rage," Burr's youthful follower[1156] shouldered the burly general "into the middle of the street." Wilkinson swallowed the insult. On learning of the incident Jackson "was wild with delight."[1157] Burr's enemies were as furious with anger. To spirited Virginians, only treason itself was worse than the refusal of Wilkinson, thus insulted, to fight. Swartwout, perhaps inspired by Jackson, later confirmed this public impression of Wilkinson's cowardice. He challenged the General to a duel; the hero refused—"he held no correspondence with traitors or conspirators," he loftily observed;[1158] whereupon the young "conspirator and traitor" denounced, in the public press, the commander of the American armies as guilty of treachery, perjury, forgery, and cowardice.[1159] The highest officer in the American military establishment "posted for cowardice" by a mere stripling! More than ever was Swartwout endeared to Jackson. Soon after his arrival at Richmond, and a week before Burr was indicted, Wilkinson perceived, to his dismay, the current of public favor that was beginning to run toward Burr; and he wrote to Jefferson in unctuous horror: "I had anticipated that a deluge of Testimony would have been poured forth from all quarters, to overwhelm Him [Burr] with guilt & dishonour—... To my Astonishment I found the Traitor vindicated & myself condemned by a Mass of Wealth Character-influence & Talents—merciful God what a Spectacle did I behold—Integrity & Truth perverted & trampled
- 82. under foot by turpitude & Guilt, Patriotism appaled & Usurpation triumphant."[1160] Wilkinson was plainly weakening, and Jefferson hastened to comfort his chief witness: "No one is more sensible than myself of the injustice which has been aimed at you. Accept I pray, my salutations and assurances of respect and esteem."[1161] Before the grand jury had indicted Burr and Blennerhassett, Wilkinson suffered another humiliation. On the very day that the General sent his wailing cry of outraged virtue to the President, Burr gave notice that he would move that an attachment should issue against Jefferson's hero for "contempt in obstructing the administration of justice" by rifling the mails, imprisoning witnesses, and extorting testimony by torture.[1162] The following day was consumed in argument upon the motion that did not rise far above bickering. Marshall ruled that witnesses should be heard in support of Burr's application, and that Wilkinson ought to be present.[1163] Accordingly, the General was ordered to come into court. James Knox, one of the young men who had accompanied Burr on his disastrous expedition, had been brought from New Orleans as a witness for the Government. He told a straightforward story of brutality inflicted upon him because he could not readily answer the printed questions sent out by Jefferson's Attorney-General.[1164] By other witnesses it appeared that letters had been improperly taken from the post-office in New Orleans.[1165] An argument followed in which counsel on both sides distinguished themselves by the learning and eloquence they displayed.[1166] It was while Botts was speaking on this motion to attach Wilkinson, that the grand jury returned the bills of indictment.[1167] So came the dramatic climax. Instantly the argument over the attachment of Wilkinson was suspended. Burr said that he would "prove that the indictment
- 83. against him had been obtained by perjury"; and that this was a reason for the court to exercise its discretion in his favor and to accept bail instead of imprisoning him.[1168] Marshall asked Martin whether he had "any precedent, where a court has bailed for treason, after the finding of a grand jury," when "the testimony ... had been impeached for perjury," or new testimony had been presented to the court.[1169] For once in his life, Martin could not answer immediately and offhand. So that night Aaron Burr slept in the common jail at Richmond. "The cup of bitterness has been administered to him with unsparing hand," wrote Washington Irving.[1170] But he did not quail. He was released next morning upon a writ of habeas corpus; [1171] the argument on the request for the attachment of Wilkinson was resumed, and for three days counsel attacked and counter- attacked.[1172] On June 26, Burr's attorneys made oath that confinement in the city jail was endangering his health; also that they could not, under such conditions, properly consult with him about the conduct of his case. Accordingly, Marshall ordered Burr removed to the house occupied by Luther Martin; and to be confined to the front room, with the window shutters secured by bars, the door by a padlock, and the building guarded by seven men. Burr pleaded not guilty to the indictments against him, and orders were given for summoning the jury to try him.[1173] Finally, Marshall delivered his written opinion upon the motion to attach Wilkinson. It was unimportant, and held that Wilkinson had not been shown to have influenced the judge who ordered Knox imprisoned or to have violated the laws intentionally. The Chief Justice ordered the marshal to summon, in addition to the general panel, forty-eight men to appear on August 3 from Wood County, in which Blennerhassett's island was located, and where the indictment charged that the crime had been committed.[1174]
- 84. Five days before Marshall adjourned court in order that jurymen might be summoned and both prosecution and defense enabled to prepare for trial, an event occurred which proved, as nothing else could have done, how intent were the people on the prosecution of Burr, how unshakable the tenacity with which Jefferson pursued him. On June 22, 1807, the British warship, the Leopard, halted the American frigate, the Chesapeake, as the latter was putting out to sea from Norfolk. The British officers demanded of Commodore James Barron to search the American ship for British deserters and to take them if found. Barron refused. Thereupon the Leopard, having drawn alongside the American vessel, without warning poured broadsides into her until her masts were shot away, her rigging destroyed, three sailors killed and eighteen wounded. The Chesapeake had not been fitted out, was unable to reply, and finally was forced to strike her colors. The British officers then came on board and seized the men they claimed as deserters, all but one of whom were American-born citizens.[1175] The whole country, except New England, roared with anger when the news reached the widely separated sections of it; but the tempest soon spent its fury. Quickly the popular clamor returned to the "traitor" awaiting trial at Richmond. Nor did this "enormity," as Jefferson called the attack on the Chesapeake,[1176] committed by a foreign power in American waters, weaken for a moment the President's determination to punish the native disturber of our domestic felicity. The news of the Chesapeake outrage arrived at Richmond on June 25, and John Randolph supposed that, of course, Jefferson would immediately call Congress in special session.[1177] The President did nothing of the kind. Wilkinson, as Commander of the Army, advised him against armed retaliation. The "late outrage by the British," wrote the General, "has produced ... a degree of Emotion bordering on rage—I revere the Honourable impulse but fear its Effects—... The present is no moment for precipitancy or a stretch of power—on
- 85. the contrary the British being prepared for War & we not, a sudden appeal to hostilities will give them a great advantage—... The efforts made here [Richmond] by a band of depraved Citizens, in conjunction with an audacious phalanx of insolent exotics, to save Burr, will have an ultimate good Effect, for the national Character of the Ancient dominion is in display, and the honest impulses of true patriotism will soon silence the advocates of usurpation without & conspiracy within." Wilkinson tells Jefferson that he is coming to Washington forthwith to pay his "respects," and concludes: "You are doubtless well advised of proceedings here in the case of Burr—to me they are incomprehensible as I am no Jurist—The Grand Jury actually made an attempt to present me for Misprision of Treason—... I feel myself between 'Scylla and Carybdis' the Jury would Dishonor me for failing of my Duty, and Burr & his Conspirators for performing it—"[1178] Not until five weeks after the Chesapeake affair did the President call Congress to convene in special session on October 26—more than four months after the occurrence of the crisis it was summoned to consider.[1179] But in the meantime Jefferson had sent a messenger to advise the American Minister in London to tell the British Government what had happened, and to demand a disavowal and an apology. Meanwhile, the Administration vigorously pushed the prosecution of the imprisoned "traitor" at Richmond.[1180] Hay was dissatisfied that Burr should remain in Martin's house, even under guard and with windows barred and door locked; and he obtained from the Executive Council of Virginia a tender to the court of "apartments on the third floor" of the State Penitentiary for the incarceration of the prisoner. Burr's counsel strenuously objected, but Marshall ordered that he be confined there until August 2, at which time he should be returned to the barred and padlocked room in Martin's house.[1181]
- 86. In the penitentiary, "situated in a solitary place among the hills" a mile and a half from Richmond,[1182] Burr remained for five weeks. Three large rooms were given him in the third story; the jailer was considerate and kind; his friends called on him every day;[1183] and servants constantly "arrived with messages, notes, and inquiries, bringing oranges, lemons, pineapples, raspberries, apricots, cream, butter, ice and some ordinary articles."[1184] Burr wrote Theodosia of his many visitors, women as well as men: "It is well that I have an ante-chamber, or I should often be gêné with visitors." If Theodosia should come on for the trial, he playfully admonishes her that there must be "no agitations, no complaints, no fears or anxieties on the road, or I renounce thee."[1185] Finally Burr asked his daughter to come to him: "I want an independent and discerning witness to my conduct and that of the government. The scenes which have passed and those about to be transacted will exceed all reasonable credibility, and will hereafter be deemed fables, unless attested by very high authority.... I should never invite any one, much less those so dear to me, to witness my disgrace. I may be immured in dungeons, chained, murdered in legal form, but I cannot be humiliated or disgraced. If absent, you will suffer great solicitude. In my presence you will feel none, whatever be the malice or the power of my enemies, and in both they abound."[1186] Theodosia was soon with her father. Her husband, Joseph Alston, now Governor of South Carolina, accompanied her; and she brought her little son, who, almost as much as his beautiful mother, was the delight of Burr's heart. During these torrid weeks the public temper throughout the country rose with the thermometer.[1187] The popular distrust of Marshall grew into open hostility. A report of the proceedings, down to the time when Burr was indicted for treason, was published in a thick pamphlet and sold all over Virginia and neighboring States. The
- 87. impression which the people thus acquired was that Marshall was protecting Burr; for had he not refused to imprison him until the grand jury indicted the "traitor"? The Chief Justice estimated the situation accurately. He knew, moreover, that prosecutions for treason might be instituted thereafter in other parts of the country, particularly in New England. The Federalist leaders in that section had already spoken and written sentiments as disloyal, essentially, as those now attributed to Burr; and, at that very time, when the outcry against Burr was loudest, they were beginning to revive their project of seceding from the Union.[1188] To so excellent a politician and so far-seeing a statesman as Marshall, it must have seemed probable that his party friends in New England might be brought before the courts to answer to the same charge as that against Aaron Burr. At all events, he took, at this time, a wise and characteristically prudent step. Four days after the news of the Chesapeake affair reached Richmond, the Chief Justice asked his associates on the Supreme Bench for their opinion on the law of treason as presented in the case of Aaron Burr. "I am aware," he wrote, "of the unwillingness with which a judge will commit himself by an opinion on a case not before him, and on which he has heard no argument. Could this case be readily carried before the Supreme Court, I would not ask an opinion in its present stage. But these questions must be decided by the judges separately on their respective circuits, and I am sure that there would be a strong and general repugnance to giving contradictory decisions on the same points. Such a circumstance would be disreputable to the judges themselves as well as to our judicial system. This suggestion suggests the propriety of a consultation on new and different subjects and will, I trust, apologize for this letter."[1189] Whether a consultation was held during the five weeks that the Burr trial was suspended is not known. But if the members of the Supreme Court did not meet the Chief Justice, it would appear to be
- 88. certain that they wrote him their views of the American law of treason; and that, in the crucial opinion which Marshall delivered on that subject more than two months after he had written to his associates, he stated their mature judgments as well as his own. It was, therefore, with a composure, unwonted even for him, that Marshall again opened court on August 3, 1807. The crowd was, if possible, greater than ever. Burr entered the hall with his son-in-law, Governor Alston.[1190] Not until a week later was counsel for the Government ready to proceed. When at last the men summoned to serve on the petit jury were examined as to their qualifications, it was all but impossible to find one impartial man among them— utterly impossible to secure one who had not formed opinions from what, for months, had been printed in the newspapers. Marshall described with fairness the indispensable qualifications of a juror.[1191] Men were rejected as fast as they were questioned—all had read the stories and editorial opinions that had filled the press, and had accepted the deliberate judgment of Jefferson and the editors; also, they had been impressed by the public clamor thus created, and believed Burr guilty of treason. Out of forty-eight men examined during the first day, only four could be accepted.[1192] While the examination of jurors was in progress, one of the most brilliant debates of the entire trial sprang up, as to the nature and extent of opinions formed which would exclude a man from serving on a jury.[1193] When Marshall was ready to deliver his opinion, he had heard all the reasoning that great lawyers could give on the subject, and had listened to acute analyses of all the authorities. His statement of the law was the ablest opinion he had yet delivered during the proceedings, and is an admirable example of his best logical method. It appears, however, to have been unnecessary, and was doubtless delivered as a part of Marshall's carefully considered plan to go to
- 89. the extreme throughout the trial in the hearing and examination of every subject.[1194] For nearly two weeks the efforts to select a jury continued. Not until August 15 were twelve men secured, and most of these avowed that they had formed opinions that Burr was a traitor. They were accepted only because impartial men could not be found. When Marshall finished the reading of his opinion, Hay promptly advised Jefferson that "the [bi]as of Judge Marshall is as obvious, as if it was [stam]ped upon his forehead.... [He is] endeavoring to work himself up to a state of [f]eeling which will enable [him] to aid Burr throughout the trial, without appearing to be conscious of doing wrong. He [Marshall] seems to think that his reputation is irretrievably gone, and that he has now nothing to lose by doing as he pleases.—His concern for Burr is wonderful. He told me many years ago, when Burr was rising in the estimation of the republican party, that he was as profligate in principle, as he was desperate in fortune. I remember his words. They astonished me. "Yet," complained Hay, "when the Gr: Jury brought in their bill the Chief Justice gazed at him, for a long time, without appearing conscious that he was doing so, with an expression of sympathy & sorrow as strong, as the human countenance can exhibit without palpable emotion. If Mr. Burr has any feeling left, yesterday must have been a day of agonizing humiliation," because the answers of the jurors had been uniformly against him; and Hay gleefully relates specimens of them. "There is but one chance for the accused," he continued, "and that is a good one because it rests with the Chief Justice. It is already hinted, but not by himself [that] the decision of the Supreme Court will no[t be] deemed binding. If the assembly of men on [Blennerhassett's is]land, can be pronounced 'not an overt act' [it will] be so pronounced."[1195]
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