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IIR Filter Structures 217
FIGURE 6.4
Biquad section structure
kth biquad is the input to the (k +1)th biquad. Now each biquad section
H k (z) can be implemented in direct form II, as shown in Figure 6.4. The
entire filter is then implemented as a cascade of biquads.
As an example, consider N =4.Figure 6.5 shows a cascade form
structure for this 4th-order IIR filter.
6.2.5 MATLAB IMPLEMENTATION
Given the coefficients {b n } and {a n } of the direct form filter, we have to
obtain the coefficients b 0 , {B k,i }, and {A k,i }. This is done by the following
function dir2cas.
function [b0,B,A] = dir2cas(b,a);
% DIRECT-form to CASCADE-form conversion (cplxpair version)
% ---------------------------------------------------------
% [b0,B,A] = dir2cas(b,a)
% b0 = gain coefficient
% B = K by 3 matrix of real coefficients containing bk’s
% A = K by 3 matrix of real coefficients containing ak’s
% b = numerator polynomial coefficients of DIRECT form
% a = denominator polynomial coefficients of DIRECT form
% compute gain coefficient b0
b0 = b(1); b = b/b0; a0 = a(1); a = a/a0; b0 = b0/a0;
%
M = length(b); N = length(a);
if N > M
b = [b zeros(1,N-M)];
FIGURE 6.5 Cascade form structure for N =4
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