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342 Chapter 7 FIR FILTER DESIGN
Ideal Impulse Response
Hamming Window
1
0.5
1
0.8
hd(n)
0
w(n)
0.6
−0.5
−1
0 5 10 15 20
n
0.4
0.2
0
0 5 10 15 20
n
h(n)
1
0.5
0
−0.5
−1
Actual Impulse Response
0 5 10 15 20
n
slope in π units
1
0.8
0.6
0.4
0.2
Amplitude Response
0
0 0.2 0.4 0.6 0.8 1
frequency in π units
FIGURE 7.23 FIR differentiator design in Example 7.12
□ EXAMPLE 7.13 Design a length-25 digital Hilbert transformer using a Hann window.
Solution
The ideal frequency response of a linear-phase Hilbert transformer is given by
{ −je −jαω
H d (e jω , 0 hd = (2/pi)*((sin((pi/2)*(n-alpha)).^2)./(n-alpha)); hd(alpha+1)=0;
>> w_han = (hann(M))’; h = hd .* w_han; [Hr,w,P,L] = Hr_Type3(h);
>> subplot(2,2,1); stem(n,hd); title(’Ideal Impulse Response’)
>> axis([-1 M -1.2 1.2]); xlabel(’n’); ylabel(’hd(n)’)
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