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500 Chapter 9 SAMPLING RATE CONVERSION
Solution
We will explore the intfilt function for the design using L = 5 and study the
effect of alpha on the filter design. The following MATLAB script provides the
detail.
I = 4; L = 5;
Hf1 = figure(’units’,’inches’,’position’,[1,1,6,4],...
’paperunits’,’inches’,’paperposition’,[0,0,6,4]);
% (a) Full signal bandwidth: alpha = 1
alpha = 1; h = intfilt(I,L,alpha);
[Hr,w,a,L] = Hr_Type1(h); Hr_min = min(Hr); w_min = find(Hr == Hr_min);
H = abs(freqz(h,1,w)); Hdb = 20*log10(H/max(H)); min_attn = Hdb(w_min);
subplot(2,2,1); plot(ww/pi,Hr,’g’,’linewidth’,1.0); axis([0,1,-1,5]);
set(gca,’xtick’,[0,1/I,1],’ytick’,[0,I]); grid; ylabel(’Amplitude’);
title(’Amplitude Response: alpha = 1’,’fontsize’,TF)
subplot(2,2,3); plot(w/pi,Hdb,’m’,’linewidth’,1.0); axis([0,1,-50,10]);
set(gca,’xtick’,[0,1/I,1],’ytick’,[-50,round(min_attn),0]); grid
ylabel(’Decibels’); xlabel(’\omega/\pi’, ’fontsize’,10);
title(’Log-mag Response: alpha = 1’,’fontsize’,TF)
% (b) Partial signal bandwidth: alpha = 0.75
alpha = 0.75; h = intfilt(I,L,alpha);
[Hr,w,a,L] = Hr_Type1(h); Hr_min = max(Hr(end/2:end)); w_min = find(Hr == Hr_min);
H = abs(freqz(h,1,w)); Hdb = 20*log10(H/max(H)); min_attn = Hdb(w_min);
subplot(2,2,2); plot(ww/pi,Hr,’g’,’linewidth’,1.0); axis([0,1,-1,5]);
set(gca,’xtick’,[0,1/I,1],’ytick’,[0,I]); grid; ylabel(’Amplitude’);
title(’Amplitude Response: alpha = 0.75’,’fontsize’,TF)
subplot(2,2,4); plot(w/pi,Hdb,’m’,’linewidth’,1.0); axis([0,1,-50,10]);
set(gca,’xtick’,[0,1/I,1],’ytick’,[-50,round(min_attn),0]); grid
ylabel(’Decibels’); xlabel(’\omega/\pi’, ’fontsize’,10);
title(’Log-mag Response: alpha = 0.75’,’fontsize’,TF)
The plots are shown in Figure 9.19. For the full bandwidth case of alpha = 1,
the filter has more ripple in both the passband and the stopband with the
minimum stopband attenuation of 22 DB. This is because the filter transition
band is very narrow. For alpha = 0.75, the filter specifications are more lenient,
and hence its response is well behaved with minimum stopband attenuation of
40 DB. Note that we do not have complete control over other design parameters.
These issues are discussed in more detail further along in this section. □
In the following example, we design a linear-phase equiripple FIR
interpolation filter using the Parks-McClellen algorithm.
□ EXAMPLE 9.8 Design an interpolator that increases the input sampling rate by a factor of
I =5.Use the firpm algorithm to determine the coefficients of the FIR filter
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