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440 Chapter 8 IIR FILTER DESIGN
Solution
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; Fs = 1/T; % Set T=1
>> OmegaP = (2/T)*tan(wp/2); % Prewarp Prototype Passband freq
>> OmegaS = (2/T)*tan(ws/2); % Prewarp Prototype Stopband freq
>> % Analog Chebyshev-2 Prototype Filter Calculation:
>> [cs,ds] = afd_chb2(OmegaP,OmegaS,Rp,As);
*** Chebyshev-2 Filter Order = 4
>> % Bilinear transformation:
>> [b,a] = bilinear(cs,ds,Fs); [C,B,A] = dir2cas(b,a)
C = 0.1797
B = 1.0000 0.5574 1.0000
1.0000 -1.0671 1.0000
A = 1.0000 -0.4183 0.1503
1.0000 -1.1325 0.7183
The desired filter is again a 4th-order filter with system function
H(z) = 0.1797 ( 1+0.5574z −1 + z −2)( 1 − 1.0671z −1 + z −2)
(1 − 0.4183z −1 +0.1503z −2 )(1− 1.1325z −1 +0.7183z −2 )
The frequency response plots are given in Figure 8.28. Note that the bilinear
transformation has properly designed the Chebyshev-II digital filter. □
□ EXAMPLE 8.20 Design the digital elliptic filter of Example 8.14. The specifications are
ω p =0.2π, R p =1dB
ω s =0.3π, A s =15dB
Solution
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; Fs = 1/T; % Set T=1
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