Digital Signal Processing Reference
In-Depth Information
Magnitude response of the bandpass filter
10
0
−
10
−
20
−
30
−
40
−
50
−
60
−
70
−
80
90
−
10
3
10
4
10
5
10
6
Frequency in rad/sec-log scale
Figure 4.14
Magnitude response of the bandpass filter in Example 4.6.
9.
The transfer function of the lowpass prototype Chebyshev filter is derived
from
H(p)
H
0
/
[
k
=
1
(p
=
−
p
k
)
]where
H
0
is fixed to match the gain
of 10 dB at
=
0:
0
.
8788
H(p)
=
(4.81)
(p
2
+
0
.
3018
p
+
1
.
009
)(p
2
+
0
.
7287
p
+
0
.
302
)
(s
2
+
10
9
)/(
9
×
10
4
s)
in
H(p)
and simplify to
10.
Now substitute
p
=
get
H(s)
5
.
7658
×
10
19
s
4
D(s)
H(s)
=
where
(s
4
+
2
.
7162
×
10
4
s
3
+
101
.
729
×
10
8
s
2
+
2
.
7162
×
10
13
s
+
10
18
)
D(s)
=
(s
4
10
4
s
3
10
8
s
2
10
13
s
10
18
)
×
+
6
.
5583
×
+
44
.
462
×
+
6
.
5583
×
+
(4.82)
To verify the design, we have plotted the magnitude response of the bandpass
filter in Figure 4.14.
4.3.3 Bandstop Filter
The normal specification of a bandstop (bandreject) filter is shown in Figure 4.15.
The passband of this filter is given by 0
≤
ω
≤
ω
1
and
ω
2
≤
ω
≤∞
, whereas
Search WWH ::
Custom Search