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Lattice Filter Structures 243
FIGURE 6.19
form
FIR filter structures in Example 6.8: (a) direct form (b) lattice
Hence
K 0 =2,K 1 = 1 4 ,K2 = 1 2 ,K3 = 1 3
The direct form and the lattice form structures are shown in Figure 6.19. To
check that our lattice structure is correct, let us compute the impulse response
of the filter using both forms.
>> [x,n] = impseq(0,0,3]; format long hdirect=filter(b,1,delta)
hdirect =
2.00000000000000 1.08333333333333 1.25000000000000 0.66666666666667
>> hlattice=latcfilt(K,delta)
hlattice =
2.00000000000000 1.08333333333333 1.25000000000000 0.66666666666667
□
6.4.3 ALL-POLE LATTICE FILTERS
A lattice structure for an IIR filter is restricted to an all-pole system
function. It can be developed from an FIR lattice structure. Let an allpole
system function be given by
H(z) =
1+
1
(6.22)
N∑
a N (m)z −m
m=1
which from (6.19) is equal to H(z) =1/A N (z). Clearly, it is an inverse system
to the FIR lattice of Figure 6.18 (except for factor b 0 ). This IIR filter
of order N has a lattice structure with N stages, as shown in Figure 6.20.
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