Digital Signal Processing Reference
In-Depth Information
0.8717
-0.3667
V2 =
0
0
0
1
The circuit realizing the third-order transfer function
A
2
(z)
in the form of a
lattice-ladder structure is shown in Figure 6.26, where the values of
V
0
=
V
1
=
V
2
=
0 as shown by the vector
V2
above.
The circuit realizing the fifth-order lowpass elliptic filter as the parallel connec-
tion of two allpass filters
A
1
(z)
and
A
2
(z)
, each realized by the lattice structures,
is shown in Figure 6.27.
Now let us compare the different circuits that we have designed to realize
a lowpass fifth-order, IIR filter. All of these circuits have been designed to
meet the following same specifications—
W
p
=
0
.
4,
W
s
=
0
.
6,
A
p
=
0
.
3, and
A
s
=
35—and have been realized by a cascade connection, a parallel con-
nection, and a lattice-ladder connection as shown in Figures 6.14, 6.15, and
6.19, respectively. They use more than the minimum number of five multipliers,
whereas the lattice-coupled allpass filter shown in Figure 6.25 uses five multipli-
ers—disregarding the multipliers with a gain of
1or
2
because they represent
−
X(z)
Σ
Σ
Σ
−
K
1
−
K
2
−
K
3
K
3
K
2
K
1
z
−
1
z
−
1
z
−
1
Σ
Σ
Σ
V
0
V
3
V
2
V
1
Y(z)
Σ
Σ
Σ
Figure 6.26
A third-order allpass filter
A
2
(z)
realized as a lattice-ladder structure.
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