Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 317

1

0.5

0

0 5 10 15 20 25 30 35 40 45

Frequency (Hz)

0

-20

-40

-60

-80

-100

0 5 10 15 20 25 30 35 40 45

Frequency (Hz)

FIGURE 8.12

Frequency responses of the designed digital filter for Example 8.6.

We simplify the algebra by dividing both the numerator and the denominator by 180:

103:92 103:92=180

z 1
z þ 1 þ 103:92=180

0:5773
z 1
z þ 1 þ 0:5773

HðzÞ¼ ¼ ¼

z 1
z þ 1 þ 103:92

180

Then we multiply both numerator and denominator by ðz þ 1Þ to obtain

0:5773ðz þ 1Þ
z 1
z þ 1 þ 0:5773

ðz 1Þþ0:5773ðz þ 1Þ ¼ 0:5773 z þ 0:5773

0:5773z þ 0:5773

z þ 1 ¼

HðzÞ¼

1:5773z 0:4227

Finally, we divide both numerator and denominator by 1:5773z to get the transfer function in the standard
format:

ð1:5773z 0:4227Þ=ð1:5773zÞ ¼ 0:3660 þ 0:3660 z 1

HðzÞ¼ ð0:5773 z þ 0:5773Þ=ð1:5773 z Þ

1 0:2679z 1

b. The corresponding MATLAB design is listed in Program 8.2. Figure 8.12 shows the magnitude and phase
frequency responses.

Program 8.2. MATLAB program for Example 8.6.
%Example 8.6
% Plot the magnitude and phase responses
fs ¼ 90; % Sampling rate (Hz)