Digital Signal Processing Reference
In-Depth Information
FIGURE 5.12.
Third-order IIR lattice filter structure with poles and zeros.
5.12 shows the equivalent IIR lattice structure. The transfer function from Figure
5.11 is
115
+
.
z
-
1
-
2
z
-
2
+
z
-
3
()
=
(5.28)
Hz
-
1
-
2
-
3
105
-
.
z
+
02
.
z
-
01
.
z
Using the results associated with an all-pole structure, and changing the coefficients
a
i
into
b
i
to reflect the denominator polynomial, (4.45) becomes
()
=+
-
1
-
2
-
3
-
1
-
2
-
3
Yz
1
bz
+
bz
+
bz
=-
1
05
.
z
+
02
.
z
-
01
.
z
3
31
32
33
Starting with
r
=
3, we have
kb
3
==-
01
.
33
Using (4.49), with
r
=
3 and
i
=
0, we have
(
)
-
(
)
bkb
k
-
-
10101
101
--
.
.
30
3
33
b
=
=
=
1
20
1
2
2
(
)
--
.
For
r
=
3 and
i
=
1, we have
(
)
--
(
)(
)
bkb
k
-
-
-
05 01 02
101
.
.
.
31
3
32
b
=
=
=-
0 0303
.
21
2
2
1
(
)
--
.
3
and, for
i
=
2,
=
(
--
(
)
-
(
)
bkb
k
-
-
02
.
01 05
101
.
.
32
3
31
b
=
=
0 1515
.
22
1
2
2
(
)
--
.
3
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