Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 337

3. Applying the BLT, the analog filter is converted into a digital filter as follows:

s¼16;000ðz1Þ=ðzþ1Þ

1:1878 10 4 s
s 2 þ 1:1878 10 4 s þ 5:7341 10 8

HðzÞ¼

This is simplified and arranged as follows:

0:1864 0:1864z 2
1 þ 0:6227z 1 þ 0:6272z 2

HðzÞ¼

b. Program 8.9 lists the MATLAB details. Figure 8.22 displays the frequency responses.

Program 8.9. MATLAB program for Example 8.13.
% Example 8.13
% Design of the digital bandpass Chebyshev filter
format long
fs ¼ 8000;
[B A] ¼ lp2bp([2.8628],[1 2.8628],sqrt(5.7341*10^8),4149) % 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 [0.1864 0.0 -0.1864]; numerator coefficients from MATLAB
%a ¼ [1 0.6227 0.6272]; denominator coefficients from MATLAB
freqz(b,a,512,fs);
axis([0 fs/2 -40 10])

10

0

-10

-20

-30

-40

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

100

50

0

-50

-100

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

FIGURE 8.22

Frequency responses of the designed digital filter for Example 8.13.