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Properties of Linear-phase FIR Filters 321
h(n)
10
5
0
Impulse Response
Hr
30
20
10
Type–4 Amplitude Response
−5
0
d(n)
10
5
0
−5
0 5 10
n
d(n) coefficients
−10
0 0.5 1
frequency in π units
imagninary axis
1
0
−1
Pole–Zero Plot
z–plane
0 5 10
n
FIGURE 7.7 Plots in Example 7.7
−1 0 1
real axis
MATLAB script:
>> h = [-4,1,-1,-2,5,6,-6,-5,2,1,-1,4];
>> M = length(h); n = 0:M-1; [Hr,w,d,L] = Hr_Type4(h);
>> b,L
d = 12 10 -4 -2 2 -8
L = 6
>> dmax = max(d)+1; dmin = min(d)-1;
>> subplot(2,2,1); stem(n,h); axis([-1 2*L+1 dmin dmax])
>> xlabel(’n’); ylabel(’h(n)’); title(’Impulse Response’)
>> subplot(2,2,3); stem(1:L,d); axis([-1 2*L+1 dmin dmax])
>> xlabel(’n’); ylabel(’d(n)’); title(’d(n) coefficients’)
>> subplot(2,2,2); plot(w/pi,Hr);grid
>> xlabel(’frequency in pi units’); ylabel(’Hr’)
>> title(’Type-1 Amplitude Response’)
>> subplot(2,2,4); pzplotz(h,1)
The plots and the zero locations are shown in Figure 7.7. From these plots, we
observe that H r (ω) iszero at ω =0.There is one zero-quadruplet constellation,
three zero pairs, and one zero at ω =0as expected.
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