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Frequency Sampling Design Techniques 353
Bandpass: M=40,T1=0.5941, T2=0.109
1
0.4
0.2
Impulse Response
Hr(k)
0.59
h(n)
0
0.109
0
0 0.2 0.35 0.65 0.8 1
frequency in π units
−0.2
−0.4
0 10 20 30 40
n
Amplitude Response
Magnitude Response
1
0
Hr(w)
0.59
Decibels
60
0.109
0
0 0.2 0.35 0.65 0.8 1
frequency in π units
0 0.2 0.35 0.65 0.8 1
frequency in π units
FIGURE 7.30 Bandpass filter design plots in Example 7.17
The optimum values of T 1 and T 2 for M =40and seven samples in the passband
[23, Appendix B] are
The MATLAB script is
T 1 =0.109021, T 2 =0.59417456
>> M = 40; alpha = (M-1)/2; l = 0:M-1; wl = (2*pi/M)*l;
>> T1 = 0.109021; T2 = 0.59417456;
>> Hrs=[zeros(1,5),T1,T2,ones(1,7),T2,T1,zeros(1,9),T1,T2,ones(1,7),T2,T1,zeros(1,4)];
>> Hdr = [0,0,1,1,0,0]; wdl = [0,0.2,0.35,0.65,0.8,1];
>> k1 = 0:floor((M-1)/2); k2 = floor((M-1)/2)+1:M-1;
>> angH = [-alpha*(2*pi)/M*k1, alpha*(2*pi)/M*(M-k2)];
>> H = Hrs.*exp(j*angH); h = real(ifft(H,M));
>> [db,mag,pha,grd,w] = freqz_m(h,1); [Hr,ww,a,L] = Hr_Type2(h);
The plots in Figure 7.30 show an acceptable bandpass filter design.
□
□ EXAMPLE 7.18 Design the following highpass filter:
Stopband edge: ω s =0.6π A s =50dB
Passband edge: ω p =0.8π R p =1dB
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