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224 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
rows in the w matrix. Finally, all the columns of the w matrix are summed
to yield the output.
function y = parfiltr(C,B,A,x);
% PARALLEL form realization of IIR filters
% ----------------------------------------
% [y] = parfiltr(C,B,A,x);
% y = output sequence
% C = polynomial (FIR) part when M >= N
% B = K by 2 matrix of real coefficients containing bk’s
% A = K by 3 matrix of real coefficients containing ak’s
% x = input sequence
%
[K,L] = size(B); N = length(x); w = zeros(K+1,N);
w(1,:) = filter(C,1,x);
for i = 1:1:K
w(i+1,:) = filter(B(i,:),A(i,:),x);
end
y = sum(w);
To obtain a direct form from a parallel form, the function par2dir can
be used. It computes poles and residues of each proper biquad and combines
these into system poles and residues. Another call of the residuez
function in reverse order computes the numerator and denominator
polynomials.
function [b,a] = par2dir(C,B,A);
% PARALLEL-to-DIRECT form conversion
% ----------------------------------
% [b,a] = par2dir(C,B,A)
% b = numerator polynomial coefficients of DIRECT form
% a = denominator polynomial coefficients of DIRECT form
% C = Polynomial part of PARALLEL form
% B = K by 2 matrix of real coefficients containing bk’s
% A = K by 3 matrix of real coefficients containing ak’s
%
[K,L] = size(A); R = []; P = [];
for i=1:1:K
[r,p,k]=residuez(B(i,:),A(i,:)); R = [R;r]; P = [P;p];
end
[b,a] = residuez(R,P,C); b = b(:)’; a = a(:)’;
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