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492 Chapter 9 SAMPLING RATE CONVERSION
I = 2, L = 5
I = 4, L = 5
2
4
Magnitude
1
Magnitude
3
2
1
0
0 0.5 1
0
0 0.25 1
I = 8, L = 5
I = 8, L = 10
8
8
Magnitude
6
4
Magnitude
6
4
2
2
0
0 0.125 1
ωπ
0
0 0.125
1
ωπ
FIGURE 9.13 Filter frequency responses in Example 9.5
% (c) Interpolation by I = 8, L = 5;
I = 8; [y,h] = interp(x,I); H = freqz(h,1,w); H = abs(H);
subplot(2,2,3); plot(w/pi,H,’g’); axis([0,1,0,I+0.4]); ylabel(’Magnitude’);
title(’I = 8, L = 5’,’fontsize’,TF); xlabel(’\omega/\pi’,’fontsize’,10)
set(gca,’xtick’,[0,0.125,1]); set(gca,’ytick’,[0:2:I]);
% (d) Interpolation by I = 8, L = 10;
I = 8; [y,h] = interp(x,I,10); H = freqz(h,1,w); H = abs(H);
subplot(2,2,4); plot(w/pi,H,’g’); axis([0,1,0,I+0.4]); ylabel(’Magnitude’);
title(’I = 8, L = 10’,’fontsize’,TF); xlabel(’\omega/\pi’,’fontsize’,10)
set(gca,’xtick’,[0,0.125,1]); set(gca,’ytick’,[0:2:I]);
The frequency response plots are shown in Figure 9.13. The first three plots
are for L = 5 and, as expected, the filters are all lowpass with passband edges
approximately around π/I frequencies and the gain of I. Also note that the
filters do not have sharp transitions and thus are not good approximations to
the ideal filter. The last plot shows the response for L = 10, which indicates
a more sharp transition, which is to be expected. Any value beyond L = 10
results in an unstable filter design and hence should be avoided.
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