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Decimation by a Factor D 485
% (c) Decimation by D = 4
D = 4; y = decimate(x,D); subplot(2,2,3);
Hc = stem(m,y(m+k1/D+1),’r’,’filled’); axis([-1,33,-1.1,1.1]);
set(Hc,’markersize’,2); ylabel(’Amplitude’);
title(’Decimated by D = 4’,’fontsize’,TF);
set(gca,’xtick’,[0,16,32]); set(gca,’ytick’,[-1,0,1]);
xlabel(’n’);
% (d) Decimation by D = 8
D = 8; y = decimate(x,D); subplot(2,2,4);
Hd = stem(m,y(m+k1/D+1),’m’,’filled’); axis([-1,33,-1.1,1.1]);
set(Hd,’markersize’,2); ylabel(’Amplitude’);
title(’Decimated by D = 8’,’fontsize’,TF);
set(gca,’xtick’,[0,16,32]); set(gca,’ytick’,[-1,0,1]);
xlabel(’n’);
From Figure 9.8, we observe that the decimated sequences for D = 2 and
D =4are correct and represent the original sinusoidal sequence x(n) atlower
sampling rates. However, the sequence for D =8is almost zero because the
Original Sequence x(n)
Decimated by D = 2
1
1
Amplitude
0
Amplitude
0
−1
0 16 32
−1
0 16 32
1
Decimated by D = 4 Decimated by D = 8
1
Amplitude
0
Amplitude
0
−1
−1
0 16 32
0 16 32
n
n
FIGURE 9.8 Original and decimated signals in Example 9.2
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