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356 Chapter 7 FIR FILTER DESIGN
1.5
Differentiator, frequency sampling design : M = 33
Hr in π units
1
0.5
0
−0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
frequency in π units
1
0.5
Impulse response
h(n)
0
−0.5
−1
0 16 32
n
FIGURE 7.32 Differentiator design plots in Example 7.19
Since this is a Type-3 linear-phase filter, the amplitude response will be zero
at ω = π. Hence to reduce the ripples, we should choose the two samples (in
transition bands) near ω = π optimally between 0 and j. Using our previous
experience, we could select this value as 0.39j. The samples of the phase response
are selected similar to those in Example 7.19.
MATLAB script:
>> M = 51; alpha = (M-1)/2; Dw = 2*pi/M; l = 0:M-1; wl = Dw*l;
>> k1 = 0:floor((M-1)/2); k2 = floor((M-1)/2)+1:M-1;
>> Hrs = [0,-j*ones(1,(M-3)/2),-0.39j,0.39j,j*ones(1,(M-3)/2)];
>> angH = [-alpha*Dw*k1, alpha*Dw*(M-k2)];
>> H = Hrs.*exp(j*angH); h = real(ifft(H,M)); [Hr,ww,a,P]=Hr_Type3(h);
The plots in Figure 7.33 show the effect of the transition band samples.
□
The SP toolbox provides a function called fir2 which combines frequency
sampling technique with the window technique to design arbitrary
shaped magnitude response FIR filters. After computing filter impulse
response using the naive design method, fir2 then applies a selected
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