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348 Chapter 7 FIR FILTER DESIGN
Frequency Samples: M=20
Impulse Response
1
0.2
Hr(k)
h(n)
0.1
0
0
0 0.2 0.3 1
frequency in π units
Amplitude Response
–0.1
0 5 10 15 20
n
Magnitude Response
1
0
Hr(w)
Decibels
16
0
0 0.2 0.3 1
frequency in π units
0 0.2 0.3 1
frequency in π units
FIGURE 7.26
Naive frequency sampling design method
>> subplot(2,2,2); stem(l,h); axis([-1,M,-0.1,0.3])
>> title(’Impulse Response’); xlabel(’n’); ylabel(’h(n)’);
>> subplot(2,2,3); plot(ww/pi,Hr,wl(1:11)/pi,Hrs(1:11),’o’);
>> axis([0,1,-0.2,1.2]); title(’Amplitude Response’)
>> xlabel(’frequency in pi units’); ylabel(’Hr(w)’)
>> subplot(2,2,4);plot(w/pi,db); axis([0,1,-60,10]); grid
>> title(’Magnitude Response’); xlabel(’frequency in pi units’);
>> ylabel(’Decibels’);
The time- and the frequency-domain plots are shown in Figure 7.26. Observe
that the minimum stopband attenuation is about 16 dB, which is clearly unacceptable.
If we increase M, then there will be samples in the transition band,
for which we do not precisely know the frequency response. Therefore the naive
design method is seldom used in practice.
□
7.4.2 OPTIMUM DESIGN METHOD
To obtain more attenuation, we will have to increase M and make the
transition band samples free samples—that is, we vary their values to
obtain the largest attenuation for the given M and the transition width.
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