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15. CH 1 CH 2 CH N
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adder
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adder (z^−1)/(1−(z^−1))
Ya(n)
−
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y(m)
FS’=FS/D
x(n)
FS
h(n)
Downsample
by
D
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31. (a)
(b)
(c)
(d)
−FS/2 0 FS/2
Frequency
FS/2D
|Hs(FS)|
−FS/2D 0
|V(FS)|
−FS/2D 0 FS/2D
|Y(FS’)|
O FS’/2FS’/2
Frequency
Frequency
Frequency
|X(FS)|
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2

32. ¦¦¥
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¤
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# 2B !¨4 g•DH !
¨are
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!¨4 ! %
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(a)
(b)
Frequency
|X(FS)|
−FS/2 FS/20
V(FS’)
Frequency
0
−FS’/2I FS’/2I 3FS’/2I
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33. Upsample
By
I
v(n)
y(m)
x(n)
FS
h(n)
FS’=IFS
b D9B@4 !…arh
£ ¤ ¨ © ¨¡¨¢ # © !# ¡ ¢ © !#¥¥% §© ¨£¢ (
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2g•)“D9)“iB@4T!…ars r
Upsample
By
I
hl(n)
Downsample
by
D
hu(n)
x(n)
Rate=Fx
Rate=IFx Rate=I/DFx=Fy
y(m)
Filter Filter
Interpolator Decimator
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34. Upsample
By
I
Downsample
by
D
x(n)
Rate=Fx
Rate=IFx Rate=I/DFx=Fy
y(m)
v(k) v(k)Filter
h(n)
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¨ ¨
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§ ¦© R'5 C'B)#w4TD9RR89!Br
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c 25RC')e#w4TDARR8A!
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ars ')#s !¨6YTDA25)dart 4T!¨ Re!S6YTDA†5!¦89UBr
5taps
sqrt(M)
M
Power =~taps*frequency
Fs
P=100Fs
50taps
sqrt(M)
Fs/sqrt(M)
Fs/M
Power=5Fs+50Fs/sqrt(M)
Decimating in Stages is Lower Power
100taps
Fs Fs/M
Power=100Fs
¦¨§©2©DD¥¤mIf0§QWc09V©V¦x)(1§Q3e9t0§4E
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arr
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ar R r
z^−1
y(n)x(n)
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'¡ ¦1#
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−100
−80
−60
−40
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Normalized Frequency (×π rad/sample)
Phase(degrees)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−10
0
10
20
30
40
50
Normalized Frequency (×π rad/sample)
Magnitude(dB)
Frequency response of an integrator
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38. y(n)x(n)
z^−k
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48. mu(l)
Ya(t)
mu(l−1)
n(l−1)Tin t(l−1) n(l)Tin t(l) Time
x(n)
y(l)
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h(n+1,mu) h(n+2,mu) h(n+3,mu)h(n,mu)
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