Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 372

After performing filter coefficient encoding, we have

ðzÞ¼ 0:7500 þ 1:484375 z 1 þ 0:7500 z 2
1 þ 1:515625z 1 þ 0:640625z 2

H q

For comparison, the uncoded zeros and encoded zeros of the transfer function HðzÞ are
Uncoded zeros: 1, 1
Coded zeros: 0.9896 þ 0.1440i, 0.9896 0.1440i
Similarly, the uncoded poles and coded poles of the transfer function H q ðzÞ are

Uncoded poles: 0.7574 þ 0.2467i, 0.7574 0.2467i
Coded poles: 0.7578 þ 0.2569i, 0.7578 0.2569i
b. The comparisons for the magnitude responses and phase responses are listed in Program 8.17 and plotted in
Figure 8.47 .
Program 8.17. MATLAB m-file for Example 8.25.

% Example 8.25
% Plot the magnitude and phase responses
fs ¼ 8000; % Sampling rate

B ¼ [0.7434 1.4868 0.7434];

A ¼ [1 1.5149 0.6346];

[hz,f] ¼ freqz(B,A,512,fs); % Calculate reponses without coefficient quantization

phi ¼ 180*unwrap(angle(hz))/pi;

Bq ¼ [0.750 1.4834375 0.75000];

0

-5

-10

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

50

0

-50

-100

-150

-200

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

FIGURE 8.47
Frequency responses (dash-dotted line, quantized coefficients; solid line, unquantized coefficients).