Digital Signal Processing Reference
In-Depth Information
z
−1
0.1
−2
+
+
z
−1
0.07
1
+
z
−1
0.065
Example 14.6
Implement the filter in Example 14.5 using the direct form II realization.
Solution
The flow graph for direct form II realization is shown in Fig. 14.21.
14.7.3 Cascaded form
The flow graph for the cascaded form is achieved by expressing the numerator
and denominator polynomials in Eq. (14.17) in terms of a product of quadratic
terms:
⌈
2
⌉
(1
+
b
1
m
z
−
1
+
b
2
m
z
−
2
)
m
=
1
H
(
z
)
=
b
0
.
(14.20)
⌈
2
⌉
(1
+
a
1
n
z
−
1
+
a
2
n
z
−
2
)
n
=
1
Factorizing
H
(
z
) in terms of quadratic terms ensures coefficients
b
1
n
and
b
2
n
to be real-valued provided that the impulse response
h
[
k
] is also real-valued.
Fig. 14.22. Cascaded form
architecture for IIR filters.
b
0
+
+
+
+
y
[
k
]
x
[
k
]
Q
(
z
)
z
−1
z
−1
b
11
a
1
q
b
1
q
a
11
+
+
+
+
z
−1
z
−1
a
2
q
a
21
b
21
b
2
q
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