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456 Chapter 8 IIR FILTER DESIGN
% Compute Analog lowpass Prototype Specifications:
T = 1; Fs = 1/T;
OmegaP = (2/T)*tan(wplp/2);
OmegaS = (2/T)*tan(wslp/2);
% Design Analog Chebyshev Prototype Lowpass Filter:
[cs,ds] = afd_chb1(OmegaP,OmegaS,Rp,As);
% Perform Bilinear transformation to obtain digital lowpass
[blp,alp] = bilinear(cs,ds,Fs);
% Transform digital lowpass into highpass filter
Nz = -[alpha,1]; Dz = [1,alpha];
[b,a] = zmapping(blp,alp,Nz,Dz);
We will demonstrate this procedure in the following example.
□ EXAMPLE 8.27 Design a highpass digital filter to satisfy
ω p =0.6π,
ω s =0.4586π,
R p =1dB
A s =15dB
Use the Chebyshev-I prototype.
Solution
MATLAB script:
>> % Digital Highpass Filter Specifications:
>> wp = 0.6*pi; % digital Passband freq in rad
>> ws = 0.4586*pi; % digital Stopband freq in rad
>> Rp = 1; % Passband ripple in dB
>> As = 15; % Stopband attenuation in dB
>> [b,a] = cheb1hpf(wp,ws,Rp,As); [C,B,A] = dir2cas(b,a)
C = 0.0243
B = 1.0000 -2.0000 1.0000
1.0000 -2.0000 1.0000
A = 1.0000 1.0416 0.4019
1.0000 0.5561 0.7647
The system function is
H(z) =
0.0243(1 − z −1 ) 4
(1+0.5661z −1 +0.7647z −2 )(1+1.0416z −1 +0.4019z −2 )
which is identical to that in Example 8.26.
□
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