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374 Chapter 7 FIR FILTER DESIGN
0.6
Impulse Response
0.4
0.2
h(n)
0
−0.2
−0.4
−0.6
0 25
n
1.5
1.2
Magnitude Response
|H|
0.6
0.4
0.1
0
0 0.1 0.2 0.3 0.4 0.5
Normalized frequency f
FIGURE 7.39 Plots of the differentiator in Example 7.27
□ EXAMPLE 7.28 Finally, we design a Hilbert transformer over the band 0.05π ≤ ω ≤ 0.95π.
Solution
Since this is a wideband Hilbert transformer, we will choose an odd length for
our filter (i.e., a Type-3 filter). Let us choose M =51. The MATLAB script is:
>> f = [0.05,0.95]; m = [1 1]; h = firpm(50,f,m,’hilbert’);
>> [db,mag,pha,grd,w] = freqz_m(h,[1]);
>> subplot(2,1,1); stem([0:50],h); title(’Impulse Response’);
>> xlabel(’n’); ylabel(’h(n)’); axis([0,50,-0.8,0.8])
>> set(gca,’XTickMode’,’manual’,’XTick’,[0,50])
>> set(gca,’YTickMode’,’manual’,’YTick’,[-0.8:0.2:0.8]);
>> subplot(2,1,2); plot(w/pi,mag); title(’Magnitude Response’)
>> xlabel(’frequency in pi units’); ylabel(’|H|’)
>> set(gca,’XTickMode’,’manual’,’XTick’,[0,f,1])
>> set(gca,’YTickMode’,’manual’,’YTick’,[0,1]);grid
The plots of this Hilbert transformer are shown in Figure 7.40.
□
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