Digital Signal Processing Reference
In-Depth Information
S
1
S
2
x
()
ym
()
Anti-aliasing
filter H1(z)
Anti-aliasing
filter H2(z)
M
1
M
2
8
240
24
FIGURE 12.16A
Multistage decimation in Example 12.4.
Solution:
M ¼
240
kHz
8 kHz
¼ 30 ¼ 10 3
We choose M
1
¼ 10 and M
2
¼ 3; there could be other choices.
Figure 12.16B
shows the block diagram and filter
frequency specifications.
Filter specifications for H
1
ðzÞ:
Passband frequency range: 0e3,400 Hz
Passband ripples: 0.05/2 ¼ 0.025 (d
p
dB ¼ 20 log
10
ð1 þ d
p
Þ¼0.212 dB)
Stopband frequency range: 20,000e120,000 Hz
Stopband attenuation: 0.005, d
s
dB ¼20 log
10
ðd
s
Þ¼46 dB
Filter type: FIR, Hamming window
Note that the lower stopband edge can be determined as
f
s
M
1
2 M
¼
240;000
f
s
240;000
2 30
f
stop
¼
¼ 20;000 Hz
10
f
stop
f
pass
f
s
¼
20;000 3;400
240;000
Df ¼
¼ 0:06917
The length of the filter and the cutoff frequency can be determined by
N ¼
3:3
Df
¼ 47:7
We choose N ¼ 49, and
f
pass
þ
f
stop
2
¼
20;000 þ 3;400
2
f
c
¼
¼ 11;700 Hz
x
()
y
()
Anti-aliasing
filter H1(z)
Anti-aliasing
filter H2(z)
10
3
f
f
0
20
40
80
120
0
4
8
12
FIGURE 12.16B
Filter frequency specifications for Example 12.4.
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