UploadFile_6417

244 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
FIGURE 6.20
All-pole lattice filter
Each stage of the filter has an input and output that are related by the
order-recursive equations [23]:
f N (n) =x(n)
f m−1 (n) =f m (n) − K m g m−1 (n − 1), m = N, N − 1,...,1
g m (n) =K m f m−1 (n)+g m−1 (n − 1), m = N, N − 1,...,1
(6.23)
y(n) =f 0 (n) =g 0 (n)
where the parameters K m , m =1, 2,...,M − 1, are the reflection coefficients
of the all-pole lattice and are obtained from (6.20) except for K 0 ,
which is equal to 1.
6.4.4 MATLAB IMPLEMENTATION
Since the IIR lattice coefficients are derived from the same (6.20) procedure
used for an FIR lattice filter, we can use the dir2latc function in
MATLAB. Care must be taken to ignore the K 0 coefficient in the K array.
Similarly, the latc2dir function can be used to convert the lattice {K m }
coefficients into the direct form {a N (m)}, provided that K 0 =1is used
as the first element of the K array. The implementation of an IIR lattice
is given by (6.23), and we will discuss it in the next section.
□ EXAMPLE 6.9 Consider an all-pole IIR filter given by
Determine its lattice structure.
1
H(z) =
1+ 13
24 z−1 + 5 8 z−2 + 1 3 z−3
Solution
MATLAB script:
>> a=[1, 13/24, 5/8, 1/3]; K=dir2latc(a)
K =
1.0000 0.2500 0.5000 0.3333
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.