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340 Chapter 7 FIR FILTER DESIGN
hd(n)
0.8
0.6
0.4
0.2
Ideal Impulse Response
w(n)
1
0.8
0.6
0.4
Kaiser Window
0
0.2
−0.2
0 10 20 30 40
n
0.8
0.6
Actual Impulse Response
0
0 10 20 30 40
n
0
Magnitude Response in dB
h(n)
0.4
0.2
Decibels
0
−0.2
0 10 20 30 40
n
60
0 1/3 2/3 1
frequency in π units
FIGURE 7.22 Bandstop filter plots in Example 7.11: β =5.9533
>> M = 45; As = 60; n=[0:1:M-1];
>> beta = 0.1102*(As-8.7)+0.3
beta = 5.9533
>> w_kai = (kaiser(M,beta))’; wc1 = pi/3; wc2 = 2*pi/3;
>> hd = ideal_lp(wc1,M) + ideal_lp(pi,M) - ideal_lp(wc2,M);
>> h = hd .* w_kai; [db,mag,pha,grd,w] = freqz_m(h,[1]);
>> subplot(2,2,1); stem(n,hd); title(’Ideal Impulse Response’)
>> axis([-1 M -0.2 0.8]); xlabel(’n’); ylabel(’hd(n)’)
>> subplot(2,2,2); stem(n,w_kai);title(’Kaiser Window’)
>> axis([-1 M 0 1.1]); xlabel(’n’); ylabel(’w(n)’)
>> subplot(2,2,3); stem(n,h);title(’Actual Impulse Response’)
>> axis([-1 M -0.2 0.8]); xlabel(’n’); ylabel(’h(n)’)
>> subplot(2,2,4);plot(w/pi,db); axis([0 1 -80 10]);
>> title(’Magnitude Response in dB’);grid;
>> xlabel(’frequency in pi units’); ylabel(’Decibels’)
The time- and the frequency-domain plots are shown in Figure 7.22, in which
the designed filter satisfies the necessary requirements.
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