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446 Chapter 8 IIR FILTER DESIGN
b0 = 0.0018
B = 1.0000 2.0000 1.0000
1.0000 2.0000 1.0000
A = 1.0000 -1.4996 0.8482
1.0000 -1.5548 0.6493
The system function is
0.0018 ( 1+z −1) 4
H(z) =
(1 − 1.4996z −1 +0.8482z −2 )(1− 1.5548z −1 +0.6493z −2 )
which is the same as in Example 8.18. The frequency-domain plots were shown
in Figure 8.27.
□
□ EXAMPLE 8.23 Digital Chebyshev-II lowpass filter design:
>> % 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:
>> T = 1; %Set T=1
>> OmegaP = (2/T)*tan(wp/2); %Prewarp Prototype Passband freq
>> OmegaS = (2/T)*tan(ws/2); %Prewarp Prototype Stopband freq
>> % Analog Prototype Order Calculation:
>> ep = sqrt(10^(Rp/10)-1); %Passband Ripple Factor
>> A = 10^(As/20); %Stopband Attenuation Factor
>> OmegaC = OmegaP; %Analog Prototype Cutoff freq
>> OmegaR = OmegaS/OmegaP; %Analog Prototype Transition Ratio
>> g = sqrt(A*A-1)/ep; %Analog Prototype Intermediate cal.
>> N = ceil(log10(g+sqrt(g*g-1))/log10(OmegaR+sqrt(OmegaR*OmegaR-1)));
>> fprintf(’\n*** Chebyshev-2 Filter Order = %2.0f \n’,N)
*** Chebyshev-2 Filter Order = 4
>> % Digital Chebyshev-II Filter Design:
>> wn = ws/pi; %Digital Stopband freq in pi units
>> [b,a]=cheby2(N,As,wn); [b0,B,A] = dir2cas(b,a)
b0 = 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
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