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512 Chapter 9 SAMPLING RATE CONVERSION
m = delay+1:1:128/D+delay+1; y = y(m); m = 0:16; y = y(16:32);
subplot(2,2,3); Hs2 = stem(m,y,’filled’); set(Hs2,’markersize’,2,’color’,’m’);
axis([-1,17,-1.2,1.2]); set(gca,’xtick’,[0:8:32]/D,’ytick’,[-1,0,1]);
title(’Output signal: y1(n): D=2’,’fontsize’,TF,’vertical’,’baseline’);
xlabel(’m’,’vertical’,’middle’); ylabel(’Amplitude’);
% Input signal x2(n) = cos(8*pi*n/16)
n = [0:256]; x = cos(8*pi*n/(16));
n1 = n(1:33); x1 = x(33:65); % for plotting purposes
subplot(2,2,2); Hs1 = stem(n1,x1,’filled’); set(Hs1,’markersize’,2,’color’,’g’);
set(gca,’xtick’,[0:8:32],’ytick’,[-1,0,1]);
axis([-2,34,-1.2,1.2]); ylabel(’Amplitude’); xlabel(’n’,’vertical’,’middle’);
Title(’Input Signal: x2(n) = cos(\pin/2)’,’fontsize’,TF,’vertical’,’baseline’);
% Decimation of x2(n): D = 2
y = upfirdn(x,[h],1,D); %y = downsample(conv(x,h),2);
m = delay+1:1:128/D+delay+1; y = y(m); m = 0:16; y = y(16:32);
subplot(2,2,4); Hs2 = stem(m,y,’filled’); set(Hs2,’markersize’,2,’color’,’m’);
axis([-1,17,-1.2,1.2]); set(gca,’xtick’,[0:8:32]/D,’ytick’,[-1,0,1]);
title(’Output signal: y2(n): D=2’,’fontsize’,TF,’vertical’,’baseline’);
xlabel(’m’,’vertical’,’middle’); ylabel(’Amplitude’);
The signal stem plots are shown in Figure 9.26. The leftside plots show the
signal x 1(n) and the corresponding decimated signal y 1(n), and the rightside
plots show the same for x 2(n) and y 2(n). In both cases the decimation appears
to be correct. If we had chosen any frequency above π/2, then the filter would
have attenuated or eliminated the signal.
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9.5.4 DESIGN SPECIFICATIONS
When we replace the ideal lowpass filter H D (ω) byafinite-order FIR filter
H(ω), we must allow for a transition band. Again we define
• ω x,p as the signal bandwidth to be preserved
• ω x,s as the frequency above which aliasing error is tolerated
Then we have 0