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458 Chapter 8 IIR FILTER DESIGN
for cheby1, cheby2, and ellip functions with appropriate modifications.
We illustrate the use of these functions through the following examples.
□ EXAMPLE 8.28 In this example we will design a Chebyshev-I highpass filter whose specifications
were given in Example 8.27.
Solution
MATLAB script:
>> % Digital Filter Specifications: % Type: Chebyshev-I highpass
>> ws = 0.4586*pi; % Dig. stopband edge frequency
>> wp = 0.6*pi; % Dig. passband edge frequency
>> Rp = 1; % Passband ripple in dB
>> As = 15; % Stopband attenuation in dB
>> % Calculations of Chebyshev-I Filter Parameters:
>> [N,wn] = cheb1ord(wp/pi,ws/pi,Rp,As);
>> % Digital Chebyshev-I Highpass Filter Design:
>> [b,a] = cheby1(N,Rp,wn,’high’);
>> % Cascade Form Realization:
>> [b0,B,A] = dir2cas(b,a)
b0 = 0.0243
B = 1.0000 -1.9991 0.9991
1.0000 -2.0009 1.0009
A = 1.0000 1.0416 0.4019
1.0000 0.5561 0.7647
The cascade form system function
H(z) =
0.0243(1 − z −1 ) 4
(1+0.5661z −1 +0.7647z −2 )(1+1.0416z −1 +0.4019z −2 )
is identical to the filter designed in Example 8.27, which demonstrates that
the two approaches described on page 386 are identical. The frequency-domain
plots are shown in Figure 8.32.
□
□ EXAMPLE 8.29 In this example we will design an elliptic bandpass filter whose specifications
are given in the following MATLAB script:
>> % Digital Filter Specifications: % Type: Elliptic Bandpass
>> ws = [0.3*pi 0.75*pi]; % Dig. stopband edge frequency
>> wp = [0.4*pi 0.6*pi]; % Dig. passband edge frequency
>> Rp = 1; % Passband ripple in dB
>> As = 40; % Stopband attenuation in dB
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