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Lowpass Filter Design Using MATLAB 445
>> % Digital Butterworth Filter Design:
>> wn = wn/pi; %Digital Butter cutoff in pi units
>> [b,a]=butter(N,wn); [b0,B,A] = dir2cas(b,a)
C = 5.7969e-004
B = 1.0000 2.0297 1.0300
1.0000 1.9997 1.0000
1.0000 1.9706 0.9709
A = 1.0000 -0.9459 0.2342
1.0000 -1.0541 0.3753
1.0000 -1.3143 0.7149
The system function is
0.00057969 ( 1+z −1) 6
H(z) =
(1 − 0.9459z −1 +0.2342z −2 )(1− 1.0541z −1 +0.3753z −2 )(1− 1.3143z −1 +0.7149z −2 )
which is the same as in Example 8.17. The frequency-domain plots were shown
in Figure 8.26.
□
□ EXAMPLE 8.22 Digital Chebyshev-I 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-1 Filter Order = %2.0f \n’,N)
*** Chebyshev-1 Filter Order = 4
>> % Digital Chebyshev-I Filter Design:
>> wn = wp/pi; %Digital Passband freq in pi units
>> [b,a]=cheby1(N,Rp,wn); [b0,B,A] = dir2cas(b,a)
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