Digital Signal Processing Reference
In-Depth Information
FIGURE 4.4.
Desired transfer function:
(
a
) lowpass;
(
b
) highpass;
(
c
) bandpass;
(
d
) bandstop.
The order of the filter is
N
=
2
Q
+
1. For example, if
Q
=
5, the filter will have 11
coefficients
h
0
,
h
1
,...,
h
10
,or
hh C
hhC
hhC
hhC
hhC
hC
==
==
==
==
==
=
0
10
5
1
9
4
2
8
3
3
7
2
4
6
1
5
0
) ideally represented for the
frequency-selective filters: lowpass, highpass, bandpass, and bandstop for which the
coefficients
C
n
Figure 4.4 shows the desired transfer functions
H
d
(
=
C
-
n
can be found.
1.
Lowpass: C
0
=
1
sin
n
n
p
p
1
Ú
()
1
CH n
=
cos
p
d
=
(4.60)
n
d
0
2.
Highpass: C
0
=
1
-
1
1
sin
n
n
p
p
Â
()
1
CH n
=
cos
p
d
=-
(4.61)
n
d
1
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