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Frequency-band Transformations 453
for l = 0:bzord-k-1
pld = conv(pld,Dz);
end
bz = bz+bZ(k+1)*conv(pln,pld);
end
az = zeros(1,aDzord+1);
for k = 0:azord
pln = [1];
for l = 0:k-1
pln = conv(pln,Nz);
end
pld = [1];
for l = 0:azord-k-1
pld = conv(pld,Dz);
end
az = az+aZ(k+1)*conv(pln,pld);
end
□ EXAMPLE 8.26 Use the zmapping function to perform the lowpass-to-highpass transformation
in Example 8.25.
Solution
First we will design the lowpass digital filter in MATLAB using the bilinear
transformation procedure and then use the zmapping function.
MATLAB script:
>> % Digital Lowpass Filter Specifications:
>> wplp = 0.2*pi; % digital Passband freq in rad
>> wslp = 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(wplp/2); % Prewarp Prototype Passband freq
>> OmegaS = (2/T)*tan(wslp/2); % Prewarp Prototype Stopband freq
>> % Analog Chebyshev Prototype Filter Calculation:
>> [cs,ds] = afd_chb1(OmegaP,OmegaS,Rp,As);
** Chebyshev-1 Filter Order = 4
>> % Bilinear transformation:
>> [blp,alp] = bilinear(cs,ds,Fs);
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