Solution Manual for Introduction to Digital Signal Processing, 1st Edition, Dick Blandford John Parr
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- 5. Solution Manual for Introduction to Digital Signal Processing, 1st Edition, Dick Blandford John Parr Ful download chapter at: https://testbankbell.com/product/solution-manual-for-introduction-to-digital- signal-processing-1st-edition-dick-blandford-john-parr/ Table of Contents 1.1 What is a digital filter? The analog circuit analysis A digital filter replacement 1.2 Overview of Analysis and Design The Analysis Process The Design Process CHAPTER 2 Discrete-Time Signals 2.0 Introduction 2.1 Discrete-Time Signals and Systems Unit Impulse and Unit Step Functions Related operations 2.2 Transformations of Discrete-Time Signals Time Transformations Amplitude Transformations 2.3 Characteristics of Discrete-Time Signals Even and Odd Signals Signals Periodic in n Signals Periodic in & 2.4 Common Discrete-Time Signals 2.5 Discrete-Time Systems 2.6 Convolution for Discrete-Time Systems Impulse representation of discrete-time signals Convolution Properties of convolution Power gain
- 6. Chapter Summary CHAPTER 3 Frequency Domain Concepts 3.0 Introduction 3.1 Orthogonal Functions and Fourier Series The Exponential Fourier Series Discrete Fourier Series 3.2 The Fourier Transform Definition of the Fourier Transform Properties of the Fourier Transform Fourier Transforms of Periodic Functions 3.3 The Discrete-Time Fourier Transform The Discrete-Time Fourier Transform (DTFT) Properties of the Discrete-Time Fourier Transform Discrete-Time Fourier Transforms of Periodic Sequences 3.4 Discrete Fourier Transform Shorthand Notation for the DFT Frequency resolution of the DFT 3.5 Fast Fourier Transform Decomposition-in-Time Fast Fourier Transform Algorithm Applications of the Discrete / Fast Fourier Transform Calculation of Fourier Transforms Convolution Calculations with the DFT/FFT Linear Convolution with the DFT Computational Efficiency 3.6 The Laplace Transform Properties of the Laplace transform Transfer functions Frequency response of continuous-time LTI systems 3.7 The z-Transform Definitions of z-Transforms z-Transforms Regions of Convergence Inverse z-Transforms z-Transform Properties
- 7. LTI System Applications Transfer Functions Causality Stability Invertibility Discrete-Time Fourier Transformz-transform Relationship Frequency Response Calculation Chapter Summary Chapter 4 Sampling and Reconstruction 4.1 Sampling Continuous-Time Signals Impulse Sampling Shannons sampling theorem Practical sampling 4.2 Anti-aliasing Filters Low pass analog Butterworth filters A low pass Butterworth analog filter has a transfer function given by Switched-capacitor filters Oversampling 4.3 The Sampling Process Errors in the sampling process 4.4 Analog to Digital Conversion Conversion techniques Successive Approximation Converter Flash Converter Sigma-Delta Conversion Error in A/D conversion process Dither 4.5 Digital to Analog Conversion D/A conversion techniques 4.6 Anti-Imaging Filters Chapter 5 FIR Filter Design and Analysis 5.1 Filter Specifications 5.2 Fundamentals of FIR Filter Design Linear phase and FIR filters
- 8. Conditions for linear phase in FIR filters Restrictions Imposed by Symmetry Window Functions and FIR Filters High pass, band pass, and band stop filters 5.3 Advanced Window Functions Kaiser Window Dolph-Chebyshev window 5.4 Frequency Sampling FIR filters 5.5 The Parks-McClellan Design Technique for FIR filters 5.6 Minimum Phase FIR filters 5.7 Applications Moving Average FIR Filter Comb Filters Differentiators Hilbert Transformers 5.8 Summary of FIR Characteristics Chapter 6 Analysis and Design of IIR Filters 6.1 Fundamental IIR design Using the Bilinear Transform Example 6.1 6.2 Stability of IIR Filters 6.3 Frequency transformations 6.4 Classic IIR filters The Butterworth Filter Chebyshev Filters Inverse Chebyshev filter Elliptic Filters Summary of Classic IIR Filters Invariant Impulse Response 6.5 Poles and Zeros in the z-Plane for IIR Filters Summary of pole and zero locations for IIR filters 6.6 Direct Design of IIR Filters Design by pole/zero placement Design of resonators and notch filters of second order Numerical Direct Design Pade method
- 9. Numerical Direct Design Prony’s method Numerical Direct Design Yule-Walker method 6.7 Applications of IIR Filters All Pass Filters IIR Moving Average Filters IIR Comb Filters Inverse Filters Chapter Summary Chapter 7 Sample Rate Conversion 7.1 Integer Decimation Frequency spectrum of the down sampled signal Cascaded Decimation 7.2 Integer Interpolation Cascaded Interpolators 7.3 Conversion by a Rational Factor 7.4 FIR Implementation Decimation filters Interpolation filters 7.5 Narrow Band Filters 7.6 Conversion by an Arbitrary Factor Hold interpolation Linear Interpolation 7.7 Bandpass Sampling 7.8 Oversampling in Audio Applications Chapter Summary Chapter 8 Realization and Implementation of Digital Filters 8.1 Implementation Issues 8.2 Number Representation Twos Complement Sign/Magnitude Floating point representation 8.3 Realization Structures FIR Structures IIR Structures
- 10. State Space Representation 8.4 Coefficient Quantization Error 8.5 Output Error due to Input Quantization 8.6 Product Quantization 8.7 Quantization and Dithering 8.8 Overflow and Scaling 8.9 Limit Cycles 8.10 DSP on Microcontrollers Microcontroller Characteristics for DSP Implementation in C FIR Implementation in C IIR Implementation in C Speed optimization Chapter 9 Digital Audio Signals 9.1 The Nature of Audio Signals 9.2 Audio File Coding Pulse Code Modulation Differential Pulse Code Modulation 9.3 Audio File Formats Lossless file format examples Lossless compressed format examples Lossy compressed format examples 9.4 Audio Effects Oscillators and signal generation Delay Flanging Chorus Tremolo and Vibrato Reverberation The Doppler Effect Equalizers Chapter Summary Chapter 10 Introduction to Two-Dimensional Digital Signal Processing 10.1 Representation of Two-Dimensional Signals
- 11. Properties of Two-Dimensional Difference Equations 10.2 Two-Dimensional Transforms The Z-Transform in Two Dimensions The two-dimensional Discrete Fourier Transform Properties of the 2D DFT The Two Dimensional DFT and Convolution The Two-Dimensional DFT and Optics The Discrete Cosine Transform in Two Dimensions 10.3 Two-Dimensional FIR Filters Window method Frequency Sampling in Two-Dimensions Transform methods Applying FIR Filters to Images Chapter Summary Chapter 11 Introduction to Wavelets 11.1 Overview 11.2 The Short Term Fourier Transform 11.3 Wavelets and the Continuous Wavelet Transform The HAAR Wavelet The Daubechies Wavelet Other Wavelet Families 11.4 Interpretation of the Wavelet Transform Data 11.5 The Undecimated Discrete Wavelet Transform 11.6 The Discrete Wavelet Transform Chapter Summary APPENDIX A Analog Filter Design A.1 Analog Butterworth Filters A.2 Analog Chebyschev Filters A.3 Analog Inverse Chebyschev Filters A.4 Analog Elliptic Filters A.5 Summary of analog filter characteristics APPENDIX B Bibliography APPENDIX C Background Mathematics C.1. Summation Formulas for Geometric Series
- 12. C.2. Eulers Relation C.3. Inverse Bilateral Z-Transforms by Partial Fraction Expansion C.4. Matrix Algebra C.5 State Variable Equations APPENDIX D MATLAB® User Functions and Commands D.1. MATLAB User Functions D.2. MATLAB Commands
- 13. Exploring the Variety of Random Documents with Different Content
- 14. Vikramâditja’s Birth. 1. Udsesskülengtu-Gôa-Chatun, a heaping up of synonyms of which we had an example, note 2, Tale XVII. Both words mean “beautiful,” “charming.” Goâ is a Mongolian expression by which royal women are called (as also chatun). Thus we sometimes meet with Udsessküleng, sometimes Udsesskülengtu (the adjunct tu forming the adjective use of the word); Udsesskülengtu-Goa, Udsesskülengtu-Chatun, or Udessküleng-Gôa-Chatun. (Jülg.) 2. Kaitja or Chaitga is a sacred grotto where relics were preserved, or marking a spot where some remarkable event of ancient date had taken place. We are told that King Ashokja (246 B.C.) caused kaitjas to be built, or rather hewn, in every spot in his dominions rendered sacred by any act of Shâkjamuni’s life67; as also over the relics of many of the first teachers (p. 390). The number of these is fabled in the Mahâvansha (v. p. 26) to have been not less than 84,000! He opened seven of the shrines in which the relics of Shâkjamuni were originally placed, and divided them into so many caskets of gold, silver, crystal, and lapis lazuli, endowing every town of his dominion with one, and building a kaitja over it. These were all completed by one given day at one and the same time, and the authority of the Dharma (law) of Buddha was proclaimed in all. In process of time great labour came to be spent on their decoration, till whole temples were hewn out of the living stone, forming almost imperishable records of the earliest architecture of the country, and to some extent of its history and religion too. The most astonishing remains are to be seen of works of this kind, with files of columns and elaborate bas-reliefs sculptured out of the solid rock. 3. Abbé Huc tells us that the Mongolians prepare their tea quite differently from the Chinese. The leaves, instead of being carefully picked as in China, are pressed all together along with the smaller tendrils and stalks into a mould resembling an ordinary brick. When required for use a piece of the
- 15. brick is broken off, pulverized, and boiled in a kettle until the water receives a reddish hue, some salt is then thrown in, and when it has become almost black milk is added. It is a great Tartar luxury, and also an article of commerce with Russia; but the Chinese never touch it. 4. An accepted token of veneration and homage. (Jülg.) 5. Sesame-oil. See note 2, Tale V. 6. Kalavinka = Sanskrit, Sperling, belongs to the sacred order of birds and scenes, in this place to be intended for the Kokila. (Jülg.) The Kokila, or India cuckoo, is as favourite a bird with Indians as the nightingale is with us. For a description of it see “A Monograph of Indian and Malayan Species of Cuculidæ,” in Journal of As. Soc. of Bengal, xi. 908, by Edward Blyth. 7. You are not to imagine that by “four parts of the universe” is meant any thing like what we have been used to call “the four quarters of the globe.” The division of the Indian cosmogony was very different and refers to the distribution of the (supposed) known universe between gods of various orders and men, to the latter being assigned the fourth and lowest called Gambudvîpa68. 8. Concerning such religious gatherings, see Köppen, i. 396, 579–583; ii. 115, 311. At such a festival held by Aravâla, King of Cashmere, on occasion of celebrating the acceptance of the teaching of Shâkjamuni as the religion of his dominion, it is said in a legend that there were present 84,000 of each order of the demigods, 100,000 priests, and 800,000 people. 9. The parrot naturally takes a prominent place in Indian fable, both on account of his sagacity, his companionable nature, and his extraordinary length of days. He did not fail to attract much notice on the part of the Greek writers on India; and Ktesias, who wrote about 370 B.C., seems to have caught some of the peculiar Indian regard for his powers, when he wrote that
- 16. though he ordinarily spoke the Indian’s language, he could talk Greek if taught it. Ælianus says they were esteemed by the Brahmans above all other birds, and that the princes kept many of them in their gardens and houses. 10. Bodhisattva. See p. 346 and note 1, Tale XI. 11. Concerning the serpent-gods, see supra, note 1 to Tale II.; and note 4, Tale XXII. 12. A legend containing curiously similar details is told in the Mahâvansha of Shishunâga, founder of an early dynasty of Magadha (Behar). The king had married his chief dancer, and afterwards sent her away. Partly out of distress and partly as a reproach she left her infant son exposed on the dunghill of the royal dwelling. A serpent-god, who was the tutelar genius of the place, took pity on the child, and was found winding its body round the basket in which it was cradled, holding its head raised over the same and spreading out its hood (it was the Cobra di capello species of serpent, which was the object of divine honours) to protect him from the sun. The people drove away the serpent-god (Nâga) with the cry of Shu! Shu! whence they gave the name of Shishunâga to the child, who, on opening the basket, was found to be endowed with qualities promising his future greatness. In this case, however, the serpent-god seems to have borne his serpent-shape, and in that of Vikramâditja, the eight are spoken of as in human form. Vikramâditja’s Youth. 1. Nirvâna. See supra, p. 330, note, p. 334, and p. 343. The word is sometimes used however poetically, simply as an equivalent for death. 2. Kütschun Tschindaktschi = “One provided with might.” (Jülg.) 3. “The custom of requiring women to go abroad veiled was only introduced after the Mussulman invasion, and was nearly the only important
- 17. circumstance in which Muhammedan influenced Indian manners.” See Lassen, Indische Alterthumskunde, iii. p. 1157. In Mongolia, however, Abbé Huc found that women have completely preserved their independence. “Far from being kept down as among other Asiatic nations they come and go at pleasure, ride out on horseback, and pay visits to each other from tent to tent. In place of the soft languishing physiognomy of the Chinese women, they present in their bearing and manners a sense of power and free will in accordance with their active life and nomad habits. Their attire augments the effect of their masculine haughty mien.” In chapter v. of vol. ii., however, he tells of a custom prevailing in part of Tibet of a much more objectionable nature than the use of a veil:—“Nearly 200 years ago the Nome-Khan, who ruled over Hither-Tibet, was a man of rigid manners.... To meet the libertinism prevailing at his day he published an edict prohibiting women from appearing in public otherwise than with their faces bedaubed with a hideous black varnish.... The most extraordinary circumstance connected with it is that the women are perfectly resigned to it.... The women who bedaub their faces most disgustingly are deemed the most pious.... In country places the edict is still observed with exactitude, but at Lha-Ssa it is not unusual to meet women who set it at defiance, ... they are, however, unfavourably regarded. In other respects they enjoy great liberty. Instead of vegetating prisoners in the depths of their houses they lead an active and laborious life.... Besides household duties, they concentrate in their own hands all the retail trade of the country, and in rural districts perform most of the labours of agriculture.” 4. Schalû. In another version of the legend he is called Sakori, the soothsayer, because he made these predictions. (Journal of As. Soc. of Bengal, vi. 350, in a paper by Lieut. W. Postans.) 5. The wolf-nurtured prince has a prominent place in Mongolian chronicles. Their dynasty was founded by Bürte-Tschinoa = the Wolf in winter-clothing. See I. J. Schmidt’s Die Völker Mittel-Asiens, vorzüglich die Mongolen und Tibeter, St. Petersburg, 1824, pp. 11–18, 33 et seq.; 70–75; and sSanang sSetsen, 56 and 372.
- 18. 6. I cannot forbear reference to notices of such sudden storms and inundations in Mongolia made from personal experience by Abbé Huc “Travels in China and Tartary,” chapters vi. and vii. 7. The persistent removal of the child after such tender entreaties and such faithful unrequited service carries an idea of heartlessness, but in extenuation it should be mentioned that while the Indians honoured every kind of animal by reason of their doctrine of metempsychosis, the wolf was just the only beast with which they seem to have had no sympathy, and they reckoned the sight of one brought ill-luck, a prejudice probably derived from the days of their pastoral existence when their approach was fraught with so much danger to their flocks. In Mongolia, where the pastoral mode of life still continues in vogue, the dread of the wolf was not likely to have diminished. Thus Abbé Huc says, “Although the want of population might seem to abandon the interminable deserts of Tartary to wild beasts, wolves are rarely met, owing to the incessant and vindictive warfare the Mongolians wage against them. They pursue them every where to the death, regarding them as their capital enemy on account of the great damage they may inflict upon their flocks. The announcement that a wolf has been seen is a signal for every one to mount his horse ... the wolf in vain attempts to flee in every direction; it meets horsemen from every side. There is no mountain so rugged that the Tartar horses, agile as goats, cannot pursue it. The horseman who has caught it with his lasso gallops off, dragging it behind, to the nearest tent; there they strongly bind its muzzle, so that they may torture it securely, and by way of finale skin it alive. In summer the wretched brute will live in this condition several days; in winter it soon dies frozen.” The wolf seems fully to return the antipathy, for (chapter xi.) he says, “It is remarkable wolves in Mongolia attack men rather than animals. They may be seen sometimes passing at full gallop through a flock of sheep in order to attack the shepherd.” 8. Tschin-tâmani, Sanskrit, “thought-jewel,” a jewel having the magic power of supplying all the possessor wishes for. Indian fable writers revel in the idea of the possession of a talisman which can satisfy all desire. The grandest and perhaps earliest remaining example of it occurs in the Ramajana, where King Visvamitra = the universal friend, who from a Xatrija
- 19. (warrior caste) merited to become a Brahman, visits Vasichtha, the chief of hermits, and finds him in possession of Sabala, a beautiful cow, which has the quality of providing Vasichtha with every thing whatever he may wish for. He wants to provide a banquet for Visvamitra, and he has only to tell Sabala to lay the board with worthy food, with food according to the six kinds of taste and drinks worthy of a king of the world. She immediately provides sugar, and honey, and rice, maireja or nectar, and wine, besides all manner of other drinks and various kinds of food heaped up like mountains; sweet fruits, and cakes, and jars of milk; all these things Sabala showered down for the use of the hosts who accompanied Visvamitra. Visvamitra covets the precious cow, and offers a hundred thousand cows of earth in barter for her. But Vasichtha refuses to part with her for a hundred million other cows or for fulness of silver. The king offers him next all manner of ornaments of gold, fourteen thousand elephants, gold chariots with four white steeds and eight hundred bells to them, eleven thousand horses of noble race, full of courage, and a million cows. The seer still remaining deaf to his offers the king carries her off by force. The heavenly cow, however, in virtue of her extraordinary qualities, helps herself out of the difficulty. It is her part to fulfil her master’s wishes, and as it is his wish to have her by him she gallops back to him, knocking over the soldiers of the earthly king by hundreds in her career. Returned to her master, the Brahman hermit, she reproaches him tenderly for letting her be removed by the earthly king. He answers her with equal affection, explaining that the earthly king has so much earthly strength that it is vain for him to resist him. At this Sabala is fired with holy indignation. She declares it must not be said that earthly power should triumph over spiritual strength. She reminds him that the power of Brahma, whom he represents, is unfailing in might, and begs him only to desire of her that she should destroy the Xatrija’s host. He desires it, and she forthwith furnishes a terrible army, and another, and another, till Visvamitra is quite undone, all his hosts, and allies, and children killed in the fray. Then he goes into the wilderness and prays to Mahâdeva, the great god, to come to his aid and give him divine weapons, spending a hundred years standing on the tips of his feet, and living on air like the serpent. Mahâdeva at last brings him weapons from heaven, at sight of which he is so elated that “his heroic courage rises like
- 20. the tide of the ocean when the moon is at the full.” With these burning arrows he devastates the whole of the beautiful garden surrounding Vasichta’s dwelling. Vasichta, in high indignation at this wanton cruelty, raises his vadschra, the Brahma sceptre or staff, and all Visvamitra’s weapons serve him no more. Then owning the fault he has committed in fighting against Brahma he goes into the wilderness and lives a life of penance a thousand years or two, after which he is permitted to become a Brahman. 9. Those who can see one and the same hero in the Sagas of Wodin, the Wild Huntsman, and William Tell69, might well trace a connexion between such a legend as this and the working of the modern law of conscription. There is no country exposed to its action where such scenes as that described in the text might not be found. There have been plenty such brought under my own notice in Rome since this “tribute of blood,” as the Romans bitterly call it, was first established there last year. 10. I have spoken elsewhere in these pages of the question of rebirth in the Buddhist system. Though not holding so cardinal a place as in Brahmanism the necessity for it remained to a certain extent. All virtues were recommended in the one case as a means to obtaining a higher degree at the next re-birth, and in the other the same, but less as an end, than as a means to earlier attaining to Nirvâna. Of all virtues the most serviceable for this purpose was the sacrifice of self for the good of the species. 11. Sinhâsana, lit. Lion-throne; a throne resting on lions, as before described in the text. 12. At the exercise of such heaven-given powers nature was supposed to testify her astonishment, and thus we are told of sacrifices and incense offered for the pacification of the same. (Jülg.) Vikramâditja acquires another Kingdom.
- 21. 1. Concerning such sacrifices, see Köppen, i. 246 and 560, and Trans. of sSanang sSetzen, p. 352. Vikramâditja makes the Silent speak. 1. The Kalmucks make the 8th, 15th, and 30th of every month fast-days; the Mongolians, the 13th, 14th, and 15th. (Köppen, i. 564–566; ii. 307–316, quoted by Jülg.) 2. Dakini. See note 2, Tale XIV., infra. 3. Dakini Tegrijin Naran = the Dakini sun of the gods. (Jülg.) 4. Aramâlâ, a string of beads used by Buddhists in their devotions. 5. Abbé Huc mentions frequently meeting with such wayside shrines, furnished just as here described. 6. Chatun. See note 1 to “Vikramâditja’s Birth.” 7. This beautiful story, which does not profess to be original, but a reproduction of one of the sagas of old, is to be found under various versions in many Indian collections of myths. 8. Compare note 3, Tale VII. 9. This story also holds a certain place among Indian legends, but is not so popular as the last. 10. Cup. No one travels or indeed goes about at all in Tibet and Mongolia without a wooden cup stuck in his breast or in his girdle. At every visit the guest holds out his cup and the host fills it with tea. Abbé Huc supplies many details concerning their use. They are so indispensable that they form a
- 22. 1 2 staple article of industry; their value varies from a few pence up to as much as 40l. 11. Tai-tsing = the all-purest, the name of the Mandschu or Mantschou dynasty (or Mangu, according to the spelling of Lassen, iv. 742), who, from being called in by the last emperor of the Ming dynasty to help in suppressing a rebellion, subsequently seized the throne (1644). This dynasty has reigned in China ever since, while the Mantchou nationality has become actually forced on the Chinese. Previously, however, the Mantchous were a tribe of Eastern Tartars long formidable to the Chinese. The introduction of a king of the Mantchous, therefore, as identical with Vikramâditja, presents the most remarkable instance that could be met with of what may be called the confusion of heroes, in the migration of myths. 12. Tsetsen Budschiktschi = the clever dancer. (Jülg.) The Wise Parrot. 1. “At any former time,” i. e. in a previous state of existence, according to the doctrine of metempsychosis. 2. “The day will come”—similarly on occasion of a subsequent rebirth. 3. Tsoktu Ilagukssan = brilliant majesty. (Jülg.) 4. Naran Gerel = sunshine. (Jülg.) 5. Ssaran = moon. (Jülg.) Lassen, Indische Alterthumskunde, ii. 67, 68. Mahavansha, ii. v. 11.
- 23. 3 4 5 6 Now called Gaya, still an important town in the province of Behar. Vihara, whence Behar (for B and V are allied sounds in Sanskrit), is the Buddhist word for a college of priests, and the substitution of Behar for Magadha, the more ancient name of the province, points to a time when Buddhism flourished there and had many such colleges (see Wilson in Journal of As. Soc. v. p. 124). Benares. Burnouf, Introd. à l’Hist. du Buddhisme, i. 157. In the far east of India and in Ceylon, where it is not indigenous, we have historical evidence that it was introduced by the Buddhists; also in Java. Lassen, Indische Alterthumskunde, i. 257; also p. 260, note 1, where he gives the following comparative descriptions of the two species, though he also points out that in ancient descriptions the characteristics of the two trees are often confused. The ficus indica or banian (it received the name of banyan from the Indian merchants, Banjans, by whose means it was propagated), is called in Bengal Njagrôdha and Vata (the Dutch call it “the devil’s tree”). The ficus religiosa is called ashvattha, and pippala. They plant the one by the side of the other with marriage ceremonies in the belief that otherwise the banian would not complete its peculiar mode of growth. Hence arises a most pleasing contrast between the elegant lightness of the shining foliage of the ficus religiosa and the solemn grandeur of the ficus indica with its picturesque trunks, its abundant leafage, its spangling of golden fruits, its pendulous roots, enabling it to reproduce itself after the fashion of a temple with countless aisles. It affords cool salubrious shade, a single one forming in time a forest to itself, and sufficing to house thousands of persons. The leaves of both supply excellent food for elephants, and birds and monkeys delight in its fruit, which, however, is not edible by man, nor is its wood of much use as timber. The pippala does not grow to nearly so great a size as the other, never attaining so many stems, but nothing can be more graceful than its appearance when, overgrowing from a building or another tree; its leaves tremble like those of the aspen (Lassen, i. 255–261, and notes). Under its overarching shade altars were erected and sacrifice offered up. To injure it wilfully was counted a sin (an instance is mentioned in Bp. Heber’s “Journey,” i. 621). A most prodigious Boddhi-tree, or rather five such growing together, still exists in Ceylon, which tradition says was transplanted thither with most extraordinary pomp and ceremonies at the time of the introduction of Buddhism into the island. They grow upon the fourth terrace of an edifice built up of successive rows of terraces, forming the most sacred spot in the whole island. Upon the above supposition this Boddhi-grove would be something like 2000 years old. Several very curious legends concerning it are given in a paper called “Remarks on the Ancient City of Anarâjapura,” by
- 24. 7 8 9 10 11 12 13 14 15 Captain Chapman, in Trans. of R. As. of Gr. Br. i. and iii. The Brahmans honoured it as well as the Buddhists, and made it a parable of the universe, its stem typifying the connexion of the visible world with a divine invisible spirit, and the up and-down growth of the branches and roots the restless striving of all creatures after an unattainable perfection; but it was the Buddhists for whom it became in the first instance actually sacred by reason of the conviction said to have been received by Shâkjamuni while observing its growth (reminding forcibly of the tradition about Sir I. Newton and the apple), that the perpetual struggles of this changeful life could only find ultimate satisfaction in that reunion with the source whence they emanated, which he termed Nirvâna. Burnouf, i. 295. Burnouf, p. 194. Nirvâna means literally in Sanskrit “the breathing out,” “extinction”—extinction of the flame of life, eternal happiness, united with the Deity. Böhtlingk and Roth’s Sanskrit Dictionary, iv. 208. In Buddhist writings, however, it is difficult to make out any idea of it distinct from annihilation. Consult Schmidt’s Trans. of sSanang sSetzen, pp. 307–331; Schott. Buddhaismus, p. 10 and 127; Köppen, i. 304–309. “Existence in the eye of Buddhism is nothing but misery.... Nothing remained to be devised as deliverance from this evil but the destruction of existence. This is what Buddhists call Nirwana.” (Alwis’ Lectures on Buddhism, p. 29.) Concerning the locality of the Malla people, see Lassen, Indische Alterthumskunde, i. 549. This word is a favourite with Buddhist writers, and means literally “him of the rolling wheel,” primarily used to denote a conqueror riding on his chariot. See Lassen, Indische Alterthumskunde, i. 810, n. 2. Lassen, ii. 52, n. 1, and 74, n. 6; and i. 356, n. 1. Professor Wilson seems to have been so much perplexed by these divergencies of chronology, that in a paper by him, published in Journ. of R. As. Soc. vol. xvi. art. 13, he endeavours to show on this (and also on other grounds) that it is possible no such person ever existed at all! See Burnouf, p. 348, n. 3; see also infra, n. 3 to “The False Friend;” also note 2 to “Vikramâditja’s Birth.” Supra, Notice of Vikramâditja, pp. 238, 239.
- 25. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 “Only about a hundred years elapsed between the visit of Fa-Hian to India and that of Soung-yun, and in the interval the absurd traditions respecting Sâkya-Muni’s life and actions would appear to have been infinitely multiplied, enlarged, and distorted.” (Lieut.- Col. Sykes’ Notes on the Religious, Moral, and Political State of Ancient India, in Journ. of R. As. Soc. No. xii. p. 280.) Turnour, in Journ. of As. Soc. of Bengal, 722. Lassen, ii. 440. Lassen, ii. 453, 454. Burnouf, Introd. a l’Hist. du Buddh. i. 137. Burnouf, Introd. &c. i. 131 et seq. “There is no reference even in the earlier Vêda to the Trimurti: to Donga, Kali, or Rama.” (Wilson, Rig-Vêda Sanhîta.) Burnouf, i. 90, 108. Lassen, ii. 426, 454, 455 and other places. “No hostile feeling against the Brahmans finds utterance in the Buddhist Canon.” (Max Müller, Anc. Sanskr. Literature.) Lassen, iv. 644, 710. Lassen, ii. 440. Lassen, iv. 646–709. As. Rec. i. 285. Genesis iii. 15. Rig-Vêda, bk. x. ch. xi. Burnouf, Introd. i. 618. See infra, Note 8 of this “Dedication;” on the word “Bede,” p. 346. Verità della Religione Cristiana-Cattolica sistematicamente dimostrata, da Monsignor Francesco Nardi U. di S. Rota. Roma, 1868. Lassen, ii. 1107. Lassen, i. 488.
- 26. 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 A great number of early authorities are quoted in Butler’s “Lives,” vol. xii., pp. 329– 334. The subject has also been handled by Gieseler, Lehrbuch der Kirchengeschichte; Wilson’s “Sketch of the Religious Sects of the Hindus;” Swainson’s “Memoir of the Syrian Christians;” most ably by A. Weber, and by many others. In note 2 of p. 182, vol. iv., Lassen quotes several authors on the meaning of the word and its identity with the triratna, as Wilson calls the Buddhist Trinity of Buddha, Dharma, and Sangha. See also infra, n. 1, Tale XVII. At the same time it presents also, of course, many frightful divergencies, and of these it may suffice to mention that the number of wives ascribed to Crishna is not less than 16,000. Lassen, vol. i. Appendix p. xxix. Indische Studien, i. 400–421, and ii. 168. The very earliest, however, do not go very far back; he was never heard of at all till within 200 B.C., and seems then to have been set up by certain Brahmans to attract popular worship, and to counteract the at that period rapidly-spreading influence of the Buddhists. See Lassen, i. 831—839. See also note 1, p. 335, supra. Lassen, iv. 575. Lassen, p. 576. “On trouvera plus tard que l’extension considérable qu’a prise le culte du Krishna n’a été qu’une réaction populaire contre celui du Buddha; réaction qui a été dirigée, ou pleinement acceptée par les Brahmanes.” Burnouf, Introd. i. p. 136, n. 1. Lassen, iv. 815–817. Lassen, iv. 576. The best account of his life and teaching is given by S. Wassiljew, of St. Petersburg, “Der Buddhismus; aus dem Russischen übersetzt,” to which I have not had access. See supra, p. 332. See infra, Note 1, Tale XI. See supra, p. 330. Concerning Serpent-worship see infra, Note 1, Tale II. Travelling Buddhist teacher. Lassen. Burnouf, Introduction à l’Histoire du Buddhisme, ii. 359.
- 27. 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 “Southward in Bede.” See Note 8. Spence Hardy, “Legends and Theories of the Buddhists,” p. 243, when mentioning this circumstance, makes the strange mistake of confounding Behar with Berar. See Note 4, “Vikramâditja’s Throne discovered.” See supra, p. 241. According to Abbé Huc’s spelling, Tchen-kis Khan. According to Abbé Huc’s spelling, Talē Lama. See the story in Note 8 to “Vikramâditja’s Youth.” See Note 4 to “Vikramâditja’s Throne discovered.” Consult C. F. Köppen, Die Lamaische Hierarchie. According to Huc’s version of his history he was not born in a Lamasery, but in the hut of a herdsman of Eastern Tibet, in the county of Amdo, south of the Kouku-Noor. This elaborate derivation, however, has been disputed, and it is more probable the name is derived from two words, signifying “the Indian ox.” In Tibet it has no name but “great ox.” Virgil, Georg. ii. 121, “Velleraque ut foliis depectant tenuia Seres;” and Pliny, H. N. vi. 20, 2, “Seres, lanicio silvarum nobiles, perfusam aqua depectentes frondium canitiem.” Also 24, 8; and xi. 26, 1. See infra, note 2 to “Vikramâditja’s Birth.” Burnouf, i. 265. See supra, p. 351 and p. 385. See Max Müller’s “Chips from a German Workshop.”
- 29. Glossary-Index. A. Abgarus, 338. Abhedja, 374. Abhigit, 386. Abhignâna-Shukuntalâ, 249. Abhimanju, 342. Abulfazl, 393, 394, 395. Âdhibuddha, Addi-Buddha, introduction of this development of Buddhist doctrine, 346; his titles, 358, 375. Aghnjâ, 375. Agni, Agnikula, 394. Agnishtoma, 372. Ahidharma-pitaka, 333. Ahriman, xiii. Airja, ix. Airjanem-Vaêgo, xiii. Akesines, the, 383.
- 30. Alexander’s invasion of India, 233; attacked by apes, 368; exports Indian hounds, 387. Aloka (Alu), 383. Alligators, 383. Altan-Somè = temple of gold, Huc, 229. Amaradeva, Amarasinha, 247, 387. Amdo-country, 348–9. Ammonites, sacred to Vishnu, 381. Ants, gold-digging, 358. Anumati, 387. Apes, their character in fable, 136; their social organization, 386; allies to Râma, 368. Apsarasas, 247. 294. Aramâlâ, 5. 296. 404. Aravâla, 399. Arbuda (Arboo), 394. Ardschi-Bordschi. 252 et seq.; meaning of name, 393; derivation, ib.; his lineage and dynasty, ib.; his date, 394; his pedigree, ib.; legends concerning him, ib.;
- 31. his character, ib.; his literary pursuits, ib. Argols, 357. 360. Arhat, Archat, institution of the rank, 330; Arhats compile the Sûtra, 333. 342. Ariaka, ix. Ârja, Ârja-bhûmi, ix. Ârjadeva, 343. Arjaka, 365. Arjavata, viii., ix. Aryans, origin of word, viii.–ix.; their language, x.; migrations, ix.–xiv.; mentioned by Ælianus, 354; their contests with aborigines, 359; mention of, in Ramajana, 368; tirthas marking events of their immigration, 372. Ashadha, 333. Ashokja, 238; inscriptions of his reign, 334; his care of the Mango, 351; serpent-worship at his date, 355; offers human sacrifice, 362; builds 84,000 kaitjas in honour of Shâkjamuni, 398. Ashvapati, 387. Ashvattha, 328.
- 32. Astrology, late introduction of, into India, 374. Astronomy, first treated as a science in India under Vikramâditja, 247–8 and 386. 390; encouragement of Bhoga to the study, 395. Asurâs, 335. 398. Asvin, 368. Attok, xi. Avantî, 390. Avatara (see Incarnations). B. Bagatur, 377. 383. Baling-cakes, 25. 59. 74. 181. 359–60. Ballabhi-Gupta dynasty, 245. Banig, 367. Banjan, Banyan, 329 (note), 368. Barss-Irbiss, 388. Bartholomew (S.) in India, 339. Bede = Tibet, 4. 344. Behar, 328. 344 and note, 373 (see also under Magadha). Benares, 328. 330.
- 33. Bengal, vii., 394. Beowulf, the Lay of, 384. Betting forbidden in the Manu, 375. Bhadrashri, 367. Bhâgavata, 396. Bhakti, 339. Bhârata, viii. Bhâratavarsha, viii., x. Bhâratides, viii. Bhartrihari, 245. Bhavishja-Purâna, 246. Bhilsa (see Bidisha). Bhismarck, 393. Bhîxu, mode of life, 199 et seq.; nickname of Buddhists, 330. 332. 381. Bhoga, 393–5. Bhogadeva, 394. Bhogakaritra, 394. Bhogaprabandha, 394. Bhota, Bhotan, Bhotanga = Tibet, 344 et seq. Bhri, viii. Bhug, 393.
- 34. Bhugji, 368. Bidisha, 250. Bodhiruma, Boddhi-tree, 329. Bodhisarma, 358. Bodhisattva, 253. 261. 271. 275. 342. 346; definition of, 366. Boudhan, Tibetian for Buddha. Brahmâ, named in Sûtra, 334; first temple to him as chief of Trimurti, 340; curious doctrine of later Buddhists concerning his creation, 346; mode of addressing him in Mongolia, 347; shrine on the Jumna, 373; Visvâmitra’s penance for offending him, 403. Brahmans, 135; why their order produced no historians, 236–8; Buddha, allied to, 327; disciple of, 328; their allegory of the ficus religiosa, 330 (note); attend Buddha’s obsequies, 332; their sacred books quoted in the Sûtra, 334, 335; friendliness with Buddhists and subsequent persecution, 335–6 and note; fall in with Christian teachers, 339–40; discourage serpent-worship, 355; creation of their caste, 367; their teaching on transmigration, 403. Brandy, mare’s milk-, 363; rice-, 11. 14. 77. 131. 166. 199. 362. Brschiss, 82. 362. Brizi, 362.
- 35. Buddha, 248. 256. 266. 245. 327 et seq. 343. 345. 348 (see also under Skâkjamuni). Buddhism, its contributions to history of India, 238–40; religion of the Kalmucks, 325; its origin, 327; first followers, 330–1; its spread and organization, 332–3; its sacred writings, 333; adoption of Brahmanical mythology, 354–5; persecution and banishment from Hindustan, 336; its spread south and east, 336; present numbers, ib.; admixture of Christian doctrines, 337–9; temporary resistance to Brahmans’ persecution, 343; Nâgârg′una’s modifications of, 343; the tripitaka, 343; introduction into Tibet and Mongolia, 344–6; fresh developments there, 346–50; the triratna, 375 (see Ceylon, China, Japan, Mexico). Bürte-Tschinoa, 401. Butter-sacrifice, 375. C. Caboolistan, xi. Calmucks (see Kalmouks). Cashmere, 237. 246. 336. 341, 342. 355. 389. 397. 399.
- 36. Castes, action on national development, 236; disregarded by Buddha, 334; legend of their institution, 367; fisher-caste, 371; lowest, 387. Ceylon, history of, 237; introduction of the Boddhi-tree, 329–30 (note); Buddhist chronology of, 332; first written collection of Sûtra, 333; introduction of Buddhism, 335; legends of Christian Missionaries, 339. 351. 352. 363; derivation of name, 370. Chaitgar (see Kaitja). Chakdja, 349. Chara, 382. Chatun, 398. China, introduction of Buddhism into, 335. 348; population of, 336. Chinese pilgrims, 335–6. 374; dynasties (see Ming, Mantchou, &c). Chongschim, 121. 366. Churmusta, 50. 204. 265. 357. Chutuktu, 122. 366. Chutuktu niduber tschi, 366. Cîtavana, 6. 351. Coins, aids to history, 232. 373. 389.
- 37. Concha, 264, 397. Contemplative life, rules of the Manu for, 390. Cotton, early use of, in India, 334. 378. Cow, estimation of Indians for, 374–5; names of, 375; the heavenly cow, 402; allegory of temporal and spiritual might, 402–3. Cranagore, 339. Creation, account of, in Vêda, 336. Crishna, late introduction of his worship, 340–1; adaptations of Christian doctrine concerning him, 340; divergences, ib. (note); delivers the palm-tree, 363; discovers pearls, 383; bears trumpet-shell, 397. Crocodiles, myths of, 383. Cuculidæ, 399. Cups, Mongolian, 404. Cycle, Mongolian, 76. 361. D. Daeva, xii. Dagju, xii. Dagoba, 396.
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