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Lattice Filter Structures 245
FIGURE 6.21
form
IIR filter structures in Example 6.9: (a) direct form (b) lattice
Hence
K 1 = 1 4 , K2 = 1 2 , and K3 = 1 3
The direct form and the lattice form structures of this IIR filter are shown in
Figure 6.21.
□
6.4.5 LATTICE-LADDER FILTERS
A general IIR filter containing both poles and zeros can be realized as
a lattice-type structure by using an all-pole lattice as the basic building
block. Consider an IIR filter with system function
M∑
b M (k)z −k
k=0
H(z) =
= B M (z)
∑
1+ N A
a N (k)z −k N (z)
k=1
(6.24)
where, without loss of generality, we assume that N ≥ M. Alatticetype
structure can be constructed by first realizing an all-pole lattice
with coefficients K m , 1 ≤ m ≤ N for the denominator of (6.24), and
then adding a ladder part by taking the output as a weighted linear
combination of {g m (n)}, asshown in Figure 6.22 for M = N. The result
is a pole-zero IIR filter that has the lattice-ladder structure. Its output is
given by
M∑
y(n) = C m g m (n) (6.25)
m=0
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