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Optimal Equiripple Design Technique 373
h(n)
0.6
0.5
0.4
0.3
0.2
0.1
0
Actual Impulse Response
−0.1
0 48
n
1
Amplitude Response
Decibels
0
60
Magnitude Response in dB
0 0.3 0.4 0.7 0.8 1
frequency in π units
×
Weighted Error
10−3
1
Hr(w)
0.5
Hr(w)
0
0
0 0.3 0.4 0.7 0.8 1
frequency in π units
−1
0 0.3 0.4 0.7 0.8 1
frequency in π units
FIGURE 7.38 Plots for equiripple staircase FIR filter in Example 7.26
Band-1: 0 ≤ f ≤ 0.1, Slope = 1 sam/cycle ⇒ 0.0 ≤|H| ≤0.1
Band-2: 0.2 ≤ f ≤ 0.3, Slope = 2 sam/cycle ⇒ 0.4 ≤|H| ≤0.6
Band-3: 0.4 ≤ f ≤ 0.5, Slope = 3 sam/cycle ⇒ 1.2 ≤|H| ≤1.5
Let the weights be equal in all bands. The MATLAB script is:
>> f = [0 0.2 0.4 0.6 0.8 1]; % in w/pi unis
>> m = [0,0.1,0.4,0.6,1.2,1.5]; % magnitude values
>> h = firpm(25,f,m,’differentiator’);
>> [db,mag,pha,grd,w] = freqz_m(h,[1]);
>> subplot(2,1,1); stem([0:25],h); title(’Impulse Response’);
>> xlabel(’n’); ylabel(’h(n)’); axis([0,25,-0.6,0.6])
>> set(gca,’XTickMode’,’manual’,’XTick’,[0,25])
>> set(gca,’YTickMode’,’manual’,’YTick’,[-0.6:0.2:0.6]);
>> subplot(2,1,2); plot(w/(2*pi),mag); title(’Magnitude Response’)
>> xlabel(’Normalized frequency f’); ylabel(’|H|’)
>> set(gca,’XTickMode’,’manual’,’XTick’,f/2)
>> set(gca,’YTickMode’,’manual’,’YTick’,[0,0.1,0.4,0.6,1.2,1.5]); grid
The frequency-domain response is shown in Figure 7.39.
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