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Lattice Filter Structures 249
Solution
MATLAB script:
>> b = [1,2,2,1] a = [1, 13/24, 5/8, 1/3]; [K,C] = dir2ladrc(b)
K =
0.2500 0.5000 0.3333
C =
-0.2695 0.8281 1.4583 1.0000
Hence
K 1 = 1 4 ,K2 = 1 2 ,K3 = 1 3 ;
and
C 0 = −0.2695, C 1 =0.8281, C 2 =1.4583, C 3 =1
IIR filter structures in Example 6.10: (a) direct form (b) lattice-
FIGURE 6.23
ladder form
The resulting direct form and the lattice-ladder form structures are shown in
Figure 6.23. To check that our lattice-ladder structure is correct, let us compute
the first 8 samples of its impulse response using both forms.
>> [x,n]=impseq(0,0,7) format long hdirect = filter(b,a,x)
hdirect =
Columns 1 through 4
1.00000000000000 1.45833333333333 0.58506944444444 -0.56170428240741
Columns 5 through 8
-0.54752302758488 0.45261700163162 0.28426911049255 -0.25435705167494
>> hladder = ladrfilt(K,C,x)
hladder =
Columns 1 through 4
1.00000000000000 1.45833333333333 0.58506944444444 -0.56170428240741
Columns 5 through 8
-0.54752302758488 0.45261700163162 0.28426911049255 -0.25435705167494
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