Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 274

As shown in Figure 7.35 , the ripples in the passband are between 1 and 1 dB. Hence, all the specifications
are met. Note that if the specification is not satisfied, we will increase the order until the stopband attenuation and
passband ripple are met.
The next example illustrates bandpass filter design.

EXAMPLE 7.16
Design a bandpass filter with the following specifications:
DSP system sampling rate ¼ 8,000 Hz
Passband ¼ 1,000e1,600 Hz
Stopband ¼ 0e600 Hz and 2,000e4,000 Hz
Passband ripple ¼ 1dB
Stopband attenuation ¼ 30 dB
Filter order ¼ 25
Solution:
From the specifications, we have three bands: a passband, a lower stopband, and an upper stopband. We perform
normalization and specify ideal magnitudes as follows:
Folding frequency:

f s =2 ¼ 8;000=2 ¼ 4; 000 Hz

For 0 Hz: 0=4; 000 ¼ 0 magnitude: 0

For 600 Hz: 600=4; 000 ¼ 0:15 magnitude: 0

For 1,000 Hz: 1; 000=4; 000 ¼ 0:25 magnitude: 1

For 1,600 Hz: 1; 600=4; 000 ¼ 0:4 magnitude: 1

For 2,000 Hz: 2; 000=4; 000 ¼ 0:5 magnitude: 0

For 4,000 Hz: 4; 000=4; 000 ¼ 1 magnitude: 0

Next, let us determine the weights:

20

d p ¼ 10 1 ¼ 0:1220

30
20

d s ¼ 10 ¼ 0:0316

Then applying Equation (7.36) , we get

d p

d s ¼ 3:86 z 39

W s
W p 10 ¼

Hence, we have

W s ¼ 39 and W p ¼ 10

We apply the Remez() routine provided by MATLAB and check performance in Program 7.11. Table 7.15 lists the
filter coefficients. The frequency responses are depicted in Figure 7.36 .
Program 7.11. MATLAB program for Example 7.16.
% Figure 7.36 ( Example 7.16)
% MATLAB program to create Figure 7.36