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508 Chapter 9 SAMPLING RATE CONVERSION
Input Signal x(n)
Amplitude Response
1
5
Amplitude
0
Amplitude
−1
1
0 4 8
n
Output Signal y(n): I = 5
0
0 0.1 0.3 1
Frequency in π units
Log–magnitude Response
0
Amplitude
0
Decibels
−1
0 20 40
m
−53
−60
0 0.1 0.3 1
Frequency in π units
FIGURE 9.23 Signal plots and filter design plots in Example 9.10
set(gca,’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[-60,round(min_attn),0]); grid
ylabel(’Decibels’); xlabel(’Frequency in \pi units’,’vertical’,’middle’);
title(’Log-magnitude Response’,’fontsize’,TF);
The signal stem plots and filter design plots are shown in Figure 9.23. The
designed filter has a minimum stopband attenuation of 53 dB, and the resulting
interpolation is accurate even with the filter order of 32.
□
9.5.3 FIR INTEGER DECIMATION
Consider the system in Figure 9.5 on page 481 in which the ideal lowpass
filter is replaced by an FIR filter H(ω), which then results in the system
shown in Figure 9.24. The relationship between Y (ω y ) and X(ω) isgiven
by (9.24), which is repeated here for convenience
Y (ω y )= 1 D
D−1
∑
k=0
(
H ω − 2πk ) (
X ω − 2πk )
; ω = ω y
D
D
D
(9.53)
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