Digital Signal Processing Reference
In-Depth Information
w
c
Frequency
(
b
)
w
c
Frequency
(
a
)
w
1
w
2
Frequency
(
c
)
w
1
Frequency
(
d
)
w
2
Figure 4.1
Magnitude responses of analog filters: (a) lowpass filter; (b) highpass filter;
(c) bandpass filter; (d) bandstop filter.
Let us select any one of the following methods to specify the IIR filters. The
recursive algorithm is given by
N
M
y(n)
=−
a(k)y(n
−
k)
+
b(k)x(n
−
k)
(4.1)
k
=
1
k
=
0
and its equivalent form is a linear difference equation:
N
M
a(k)y(n
−
k)
=
b(k)x(n
−
k)
;
a(
0
)
=
1
(4.2)
k
=
0
k
=
0
The transfer function of the IIR filter is given by
k
=
0
b(k)z
−
k
k
=
0
a(k)z
−
k
;
H(z)
=
a(
0
)
=
1
(4.3)
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