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Partial Fraction Expansion: residuez.m

Figure J.5 gives a listing of a matlab function for computing a ``left-justified'' partial fraction expansion (PFE) of an IIR digital filter $ H(z)=B(z)/A(z)$ as described in §6.8 (and below). This function, along with its ``right justified'' counterpart, residued, are included in the octave-forge matlab library for Octave.J.1

Figure J.5: Matlab/Octave function for computing the partial fraction expansion of an IIR digital filter.

 
function [r, p, f, m] = residuez(B, A, tol)
if nargin<3, tol=0.001; end
NUM = B(:)'; DEN = A(:)';
% Matlab's residue does not return m (implied by p):
[r,p,f,m]=residue(conj(fliplr(NUM)),conj(fliplr(DEN)),tol);
p = 1 ./ p;
r = r .* ((-p) .^m);
if f, f = conj(fliplr(f)); end

This code was written for Octave, but it also runs in Matlab if the 'm' outputs (pole multiplicity counts) are omitted (two places). The input arguments are compatible with the existing residuez function in the Matlab Signal Processing Toolbox.



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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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