Digital Signal Processing Reference
In-Depth Information
from which
kb
2
==
0 1515
.
22
From (4.45), with
r
=
2 and
i
=
1,
()
=+
(
)
+
(
)
Yz
1
bz
-
1
+
bz
-
2
=+-
1
0 0303
.
z
-
1
0 1515
.
z
-
2
2
21
22
From (4.49), with
r
=
2 and
i
=
1,
(
)
-
(
)
-
(
)
bkb
k
-
-
-
0 0303
.
0 1515
.
0 0303
.
21
2
21
b
=
=
=-
0 0263
.
11
2
2
1
-
(
)
1
0 1515
.
from which
kb
1
==-
0 0263
.
11
The
k
-parameters
k
1
,
k
2
, and
k
3
provide the solution for the top half of the IIR lattice
structure in Figure 5.12. We can now use the recursive relationship in (5.27) to
compute the
c
i
coefficients that will give us the bottom part of the structure in Figure
5.12. We will now use both
a
's and
b
's in applying (4.49). Here, from the numerator
polynomial (with
a
ri
replaced by
a
i
) in (5.28),
a
a
a
a
=
=
=-
=
1
15
2
0
.
1
2
1
3
and, from the denominator polynomial in (5.28),
b
b
b
=-
=
=-
05
02
01
.
31
.
32
.
33
Starting with
c
3
and working backwards using (5.27), the coefficients
c
i
can be found,
or
ca
ca cb
ca cb cb
==
=-
{
1
3
3
(
)
=-
=- -
2
1
-
05
.
15
.
2
2
3
31
{
}
=-
+
1
1
2
21
3
32
{
}
(
)
-
(
)
+
()(
)
=--
1 5
.
1 5
.
0 0303
.
1 0 2
.
=
=-
1 2545
.
{
}
ca cbcb cb
+
+
0
0
1
11
2
22
3
33
{
}
=-
(
)
-
(
)
+-
(
)(
)
+
()
-
(
)
1
1 2545
.
0
.
0263
1 5
.
0 1515
.
1
0 1
.
=
1 3602
.
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