Digital Signal Processing Reference
In-Depth Information
Table 6.2
Frequency Response Calculations in Example 6.11
Hðe
j
U
Þ
Hðe
j
U
Þ
dB
f [
2
(radians)
p
f
s
(Hz)
:
Hðe
j
U
Þ
U
0
0.670
3.479 dB
0
0
0
1,000
0.715
2.914 dB
0
:
25
p
14
:
64
0
2,000
0.894
0.973 dB
57
0
0
:
50
p
26
:
3,000
1.357
2.652 dB
68
0
0
:
75
p
28
:
4,000
2.000
6.021 dB
0
0
1
:
00
p
Therefore, the magnitude frequency response and phase response are given by
H
e
j
U
¼
1
ð1 þ 0:5 cos ð
U
ÞÞ
2
þð0:5 sin ð
U
ÞÞ
2
q
and
:
Hðe
j
U
Þ¼tan
1
0:5 sin ð
U
Þ
1 þ 0:5 cos ð
U
Þ
Several points for the magnitude response and phase response are calculated and shown in
Table 6.2
.
The
magnitude response and phase response of the DSP system are roughly plotted in
Figure 6.15
in accordance with
the obtained data.
10
5
0
-5
-10
0
0.5
1
1.5
2
2.5
3
Frequency (radians)
40
30
20
10
0
-10
0
0.5
1
1.5
2
2.5
3
Frequency (radians)
FIGURE 6.15
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