Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 330

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Frequency (Hertz)

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Frequency (Hertz)

FIGURE 8.19

Frequency responses of the designed digital filter for Example 8.10.

After algebra simplification, it follows that

HðzÞ¼ 0:1327 0:2654 z 1 þ 0:1327 z 2
1 þ 0:7996z 1 þ 0:3618z 2

b. MATLAB Program 8.6 is listed for this example, and frequency responses are given in Figure 8.19 .

Program 8.6. MATLAB program for Example 8.10.

% Example 8.10
% Design of the digital lowpass Chebyshev filter
format long
fs ¼ 8000; % Sampling rate

% BLT design
[B A] ¼ lp2hp([1.4314],[1 1.4256 1.5162], 3.8627*10^4) % Complete step 2
[b a] ¼ bilinear(B,A,fs) % Complete step 3

% Plot the magnitude and phase responses j H(z) j
%b ¼ [0.1327 -0.2654 0.1327]; numerator coefficients from MATLAB
%a ¼ [1 0.7996 0.3618]; denominator coefficients from MATLAB
freqz(b,a,512,fs);
axis([0 fs/2 -40 10])