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IIR Filter Design&
FIR Filter Design
Utkarsh KulshresthaKuldeep Saini
IIR FilterFilters are used to remove the noise from the
baseband signals.
Filters gives the flat and smooth frequency responses.
IIR filters are the Infinite impulse response filters.
Filters are of basically two types:-1.Analog filter2. Digital filters
IIR Filterss.no.
Analog Filters Digital Filter
1. Process analog input and analog output
Process digital input and digital output
2. Constructed from active and passive electronic component
Constructed from adder,multiplier and delay unit
3. Described by a differential equations
Described by difference equation
4. Frequency response is changed by varying components
Frequency response is changed by filter cofficient
IIR FilterIIR design methods are as follows:-
1.Impulse Invariant method
2.Billinear method
3.Approximation of Derivatives
Impulse invariant method
IIR FiltersBilinear Transformation:-
1- Bilinear transformation is transformation from analog s-plane to digital z-plane.
2-It avoid the alising problem occurs in impulse invariant method.
3-This conversion maps analog poles to digital poles and analog zeros to digital
zeros.
IIR Filter
• Prewrapping Procedure:-
• Amplitude response of digital filter is expanded at the lower frequencies and compressed at the higher frequencies in comparision to the analog filter.
• Steps to design digital digital filter using bilinear transformation technique :-
• 1-find prewrapping analog frequency W=2/T tan(w/2)• 2-using analog frequencies find H(s)• 3-select the sampling rate of digital filter substitute S=2/T(1-inv z/1+inv z)Into transfer function H(s)
Butterworth Filter
The butterworth filter has magnitude frequency response is flat in passband and stopband.
As the filter order increases then the butterworth response approximates the ideal filter response.
Chebyshev filterType-1 Chebyshev filter they have equiripple behavior In passband and monotonic characterstics in stop band.
Type-2 Chebyshev filter the magnitude response has maximally in passband and equiripple in stop band.
Chebyshev filter• Type-1
Butterworth Filter
Chebyshev Filter
FIR filterIt is a Digital filter which has Finite Impulse response duration.
They have usually no feedback.
It has finite number of non zero terms.
FIR filters are used where linear phase response in passband is required.
It is used for data transmission, speech processing and always stable.
Design technique for FIR filter
1. Fourier series method2. Windowing method
Rectangular windowRaised cosine windowHamming windowHanning windowBlackmann window
Bartlett windowKaiser window
3.Frequency sampling method
Filter Design by Windowing• Simplest way of designing FIR filters• Method is all discrete-time no continuous-time involved• Start with ideal frequency response
• Choose ideal frequency response as desired response• Most ideal impulse responses are of infinite length• The easiest way to obtain a causal FIR filter from ideal is
• More generally
n
njd
jd enheH
deeH21
nh njjdd
else0
Mn0nhnh d
else0
Mn01nw where nwnhnh d
351M Digital Signal Processing
Properties of Windows• Prefer windows that concentrate around DC in frequency
– Less distortion, closer approximation
• Prefer window that has minimal span in time – Less coefficient in designed filter, computationally efficient
• So we want concentration in time and in frequency– Contradictory requirements
• Example: Rectangular window
2/sin2/1Msin
ee1
e1eeW 2/Mj
j
1MjM
0n
njj
Rectangular Window
else0
Mn01nw
• Narrowest main lob– 4/(M+1)– Sharpest transitions at
discontinuities in frequency
• Large side lobs– -13 dB– Large oscillation
around discontinuities
• Simplest window possible
18
Bartlett (Triangular) Window
else0
Mn2/MM/n22
2/Mn0M/n2
nw
• Medium main lob– 8/M
• Side lobs– -25 dB
• Hamming window performs better
• Simple equation
Hanning Window
else0
Mn0M
n2cos1
21
nw
• Medium main lob– 8/M
• Side lobs– -31 dB
• Hamming window performs better
• Same complexity as Hamming
Hamming Window
else0
Mn0M
n2cos46.054.0nw
• Medium main lob– 8/M
• Good side lobs– -41 dB
• Simpler than Blackman
21
Kaiser Window Filter Design Method• Parameterized equation
forming a set of windows– Parameter to change main-
lob width and side-lob area trade-off
– I0(.) represents zeroth-order modified Bessel function of 1st kind
otherwise
MnalphaIBetaInw
,0
2\1||),(|)({
Determining Kaiser Window Parameters• Given filter specifications Kaiser developed empirical
equations– Given the peak approximation error or in dB as A=-20log10
– and transition band width
• The shape parameter alpha should be
• The filter order M is determined approximately by
210
50212107886.0215842.0
507.81102.04.0
A
AAA
AA
alpha
FpFsF
1
F
FDM
Example: Kaiser Window Design of a Lowpass Filter• Specifications• Window design methods assume• Determine cut-off frequency
– Due to the symmetry we can choose it to be
• Compute
• And Kaiser window parameters
• Then the impulse response is given as
001.0,01.0,6.0,4.0 21pp 001.021
5.0c
2.0ps 60log20A 10
653.5alpha 37M
else0
Mn0653.5I
5.185.18n
1653.5I
5.18n5.18n5.0sinnh
0
2
0
24
Example Cont’d
Comparison of IIR & FIR filters
Copyright (C) 2005 Güner Arslan 351M Digital Signal Processing 25
s.no.
characterstics IIR FIR
1. Unit sample response Infinite duration Finite duration
2. Feedback characterstics
Use feedback from the output
Do not use feedback
3. Phase characterstics Non-linear phase response
Linear phase response
4. Number of computations
Less computations More computations
5. Applications Used where sharp cut-off characterstics with minimum order are required
Used where linear phase characterstics are required
More on FIR & IIR Next time…