Partial Fraction Expansion: residued.m

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Partial Fraction Expansion: residued.m

Figure J.9 gives a listing of a matlab function for computing a ``right justified'' partial fraction expansion (PFE) of an IIR digital filter as described in §6.8 (and below).

The code in Fig.J.9 was written to work in Octave, and also in Matlab if the 'm' argument is omitted (in two places).

**Figure J.9:** Matlab/Octave function for computing the group delay of a digital filter.
function [r, p, f, e] = residued(b, a, toler) if nargin<3, toler=0.001; end NUM = b(:)'; DEN = a(:)'; nb = length(NUM); na = length(DEN); f = []; if na<=nb f = filter(NUM,DEN,[1,zeros(nb-na)]); NUM = NUM - conv(DEN,f); NUM = NUM(nb-na+2:end); end [r,p,f2,e] = residuez(NUM,DEN,toler);

Figure J.9: Matlab/Octave function for computing the group delay of a digital filter.

function [r, p, f, e] = residued(b, a, toler)
if nargin<3, toler=0.001; end
NUM = b(:)';
DEN = a(:)';
nb = length(NUM);
na = length(DEN);
f = [];
if na<=nb
  f = filter(NUM,DEN,[1,zeros(nb-na)]);
  NUM = NUM - conv(DEN,f);
  NUM = NUM(nb-na+2:end);
end
[r,p,f2,e] = residuez(NUM,DEN,toler);

Subsections

Method

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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Introduction to Digital Filters
Matlab Utilities
Partial Fraction Expansion: residued.m