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Properties of Linear-phase FIR Filters 317
>> a,L
a = 6 10 -4 -2 2 -8
L = 5
>> amax = max(a)+1; amin = min(a)-1;
>> subplot(2,2,1); stem(n,h); axis([-1 2*L+1 amin amax])
>> xlabel(’n’); ylabel(’h(n)’); title(’Impulse Response’)
>> subplot(2,2,3); stem(0:L,a); axis([-1 2*L+1 amin amax])
>> xlabel(’n’); ylabel(’a(n)’); title(’a(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 7.4. From these plots, we
observe that there are no restrictions on H r (ω) either at ω =0orat ω = π.
There is one zero-quadruplet constellation and three zero pairs.
□
□ EXAMPLE 7.5 Let h(n) = {−4, 1, −1, −2, 5, 6, 6, 5, −2, −1, 1, −4}. Determine the amplitude
↑
response H r (ω) and the locations of the zeros of H (z).
10
Impulse Response
20
Type–1 Amplitude Response
5
10
h(n)
0
Hr
0
−5
−10
0 5 10
n
−20
0 0.5 1
frequency in π units
10
a(n) coefficients
Pole–Zero Plot
z–plane
a(n)
5
0
−5
imaginary axis
1
0
−1
0 5 10
n
FIGURE 7.4 Plots in Example 7.4
−1 0 1
real axis
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