filter design

TOPIC:-FILTER DESIGN
By
Nehe Pradeepkumar
Dattatraya

 Introduction.
 IIR Filter Design by Impulse invariance method.
 IIR Filter Design by Bilinear transformation method.
 FIR Filter Design by Frequency sampling technique.
 Advantages and Disadvantages.

 Filter:- The systm that modify the spectral contents of the
input signal are termed as filter.
 Filters mainly are of two types
1-Analog Filter
2-Digital Filter
Filter
Analog Filter
Digital Filter
FIR Filter
IIR Filter

 Performance of digital filter can not influenced due to
component ageing, temp, &power supply variations
 Highly immune to noise.
 Operated over wide range of frequency.
 Multiple filtering possible only in digital filter.

 Now we will introduce to the design method of the
FIR filter and IIR filter respectively.
 IIR is the infinite impulse response abbreviation.
 Digital filters by the accumulator, the multiplier, and
it constitutes IIR filter the way, generally may divide
into three kinds, respectively is Direct form, Cascade
form, and Parallel form.
 IIR filter design methods include the impulse
invariance, bilinear transformation.

 FIR is the finite impulse response abbreviation,
because its design construction has not returned to the
part which gives.
 Its construction generally uses Direct form and
Cascade form.
 FIR filter design methods include the window
function, frequency sampling.

Steps:
s z transformation
Step 1: let the impulse response of analog filter is h(t)
Given the transfer function in S-domain, find the
impulse response h(t).
Step 2: Sample h(t) to get h(n).
unit sample response can be obtained by putting
t=nT
Step 3: Find H(Z), by taking z-transform of h(n).

 The most straightforward of these is the impulse
invariance transformation
 Let h(t) be the impulse response corresponding to
H(s), and define the continuous to discrete time
transformation by setting h(n)=h(nT)
We sample the continuous time impulse response to
produce the discrete time filter

 The impulse invariance transformation does map the
jώ-axis and the left-half s plane into the unit circle
and its interior, respectively.

 The most generally useful is the bilinear
transformation.
 To avoid aliasing of the frequency response as
encountered with the impulse invariance
transformation.
We need a one-to-one mapping from the s plane to
the z plane.
 The problem with the transformation is
many-to-one.
s 'T z  e

We could first use a one-to-one transformation from
s to s’ , which compresses the entire s plane into the
strip
 
  Im(s ')

T T
 Then s’ could be transformed to z by
with no effect from aliasing.
s 'T z  e

 The transformation from s to s’ is given by

1 2
sT
 
' tanh ( )
2
s
T
 The characteristic of this transformation is seen most
readily from its effect on the jώ axis. Substituting
s=jώ and s’= jώ’ , we obtain
1 2
T
' tan ( )
2
T

  

 The discrete-time filter design is obtained from the
continuous-time design by means of the bilinear
transformation
H ( z ) H ( s ) | c s  T  z  
z
 1 1 (2/ )(1 )/(1 )


' ( ) d H 
 For arbitrary, non-classical specifications of , the
calculation of hn
() , n=0,1,…,M, via an appropriate
d approximation can be a substantial computation task.
 It may be preferable to employ a design technique
that utilizes specified values of H ' ( 
) directly,
d without the necessity of determining
() d hn

We wish to derive a linear phase IIR filter with real
nonzero h(n) . The impulse response must be
symmetric
M
[ /2]
k n
 
h n A A


( )  
2 cos( )
0

1
2 ( 1/ 2)
1
k
k
M
where are real and denotes the integer part
k A[ / 2] M

 It can be rewritten as

h n A e e  
 
 where N=M+1 and
Therefore, it may write

 
h n h n
( ) ( )
where
1
/ 2 /
0
/2
( )
N
j k N j kn N
k
k

k 
N
k N k A A 
1
0
/2
N
k
k

k 
N
/ 2 / ( ) j k N j kn N
k k h n A e e   

 with corresponding transform
N

 
H z H z
( ) ( )
where
 Hence
1
k
0
k N
/2
k


j 
k /
N N
A e z

(1 )
H z


k j k N
2 / 1
( )
k
1


e z

sin 
/ 2
' ( )
 ( 1)/2 which has a linear phase
sin[( / / 2)]
j T N
k k
TN
H A e
k N T

 
  


 The only nonzero contribution to H'(  ) at  
 is
k from , and hence that
'( ) k H  '( )k k H   N A
 Therefore, by specifying the DFT samples of the
desired magnitude response at the
H ' () 
d frequencies , and setting
k 
' ( ) / k d k A   H  N

We produce a filter design from equation for which
H '(k )  Hd' (k )
 The desired and actual magnitude responses are equal
at the N frequencies
k 

 In between these frequencies, is interpolated as
H '()
the sum of the responses , and its magnitude
does not, equal that of
' () k H 
' () d H 

 FIR advantage:
1. Finite impulse response
2. It is easy to optimalize
3. Linear phase
4. Stable
 FIR disadvantage:
1. It is hard to implementation than IIR

 IIR advantage :
1. It is easy to design
2. It is easy to implementation
 IIR disadvantage:
1. Infinite impulse response
2. It is hard to optimalize than FIR
3. Non-stable

filter design

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filter design