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430 Chapter 8 IIR FILTER DESIGN
Solution
The design procedure is described in the following MATLAB script:
>> % Digital Filter Specifications:
>> wp = 0.2*pi; % digital Passband freq in rad
>> ws = 0.3*pi; % digital Stopband freq in rad
>> Rp = 1; % Passband ripple in dB
>> As = 15; % Stopband attenuation in dB
>> % Analog Prototype Specifications: Inverse mapping for frequencies
>> T = 1; % Set T=1
>> OmegaP = wp / T; % Prototype Passband freq
>> OmegaS = ws / T; % Prototype Stopband freq
>> % Analog Chebyshev-1 Prototype Filter Calculation:
>> [cs,ds] = afd_chb1(OmegaP,OmegaS,Rp,As);
*** Chebyshev-1 Filter Order = 4
>> % Impulse Invariance transformation:
>> [b,a] = imp_invr(cs,ds,T); [C,B,A] = dir2par(b,a)
C = []
B =-0.0833 -0.0246
0.0833 0.0239
A = 1.0000 -1.4934 0.8392
1.0000 -1.5658 0.6549
The desired filter is a 4th-order Chebyshev-I filter whose system function H(z)is
H(z) =
−0.0833 − 0.0246z −1
1 − 1.4934z −1 +0.8392z + −0.0833 + 0.0239z −1
−2 1 − 1.5658z −1 +0.6549z −2
The frequency response plots are given in Figure 8.22.
□
□ EXAMPLE 8.13 Design a lowpass digital filter using a Chebyshev-II prototype to satisfy
ω p =0.2π, R p =1dB
ω s =0.3π, A s =15dB
Solution
Recall that the Chebyshev-II filter is equiripple in the stopband. It means that
this analog filter has a response that does not go to zero at high frequencies in
the stopband. Therefore after impulse invariance transformation, the aliasing
effect will be significant; this can degrade the passband response. The MATLAB
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