Digital Signal Processing Reference
In-Depth Information
(a)
400
H(
ω
)
300
200
100
0
−1.5
−1
−0.5
0
0.5
1
1.5
x 10
4
(b)
150
100
50
0
−4000
−3000
−2000
−1000
0
1000
2000
3000
4000
Frequency, Hz
Fig. 5.9
Example 1: decimation of an audio signal
This so-called interpolation filter should be an ideal low-pass filter with a cutoff
frequency of p/L. The block diagram of an interpolator is shown in Fig.
5.10
.
In the time-domain the L-times up-sampling operation is characterised in (
5.2
).
This operation can be re-written as
u
2
ð
Lp
Þ¼
x
ð
p
Þ;
where p
¼
0
;
1
;
2
;
...
ð
5
:
18
Þ
The final interpolation filter output is
y
ð
n
Þ¼
X
1
x
ð
p
Þ
h
ð
n
Lp
Þ:
ð
5
:
19
Þ
p
¼1
Fig. 5.10
Interpolator
u
2
n
)
L
H
(
z
)
y
(
n
)
x
(
n
)
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