Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


Software for Partial Fraction Expansion

Figure 6.3 illustrates the use of residuezJ.5) for performing a partial fraction expansion on the transfer function

$\displaystyle H(z) \eqsp \frac{1 + 0.5^3 z^{-3}}{1 + 0.9^5z^{-5}}
$

The complex-conjugate terms can be combined to obtain two real second-order sections, giving a total of one real first-order section in parallel with two real second-order sections, as discussed and depicted in §3.12.

Figure 6.3: Use of residuez to perform a partial fraction expansion of an IIR filter transfer function $ H(z)=B(z)/A(z)$ .

 
B = [1 0 0 0.125];
A = [1 0 0 0 0 0.9^5];
[r,p,f] = residuez(B,A)
% r =
%   0.16571 
%   0.22774 - 0.02016i
%   0.22774 + 0.02016i
%   0.18940 + 0.03262i
%   0.18940 - 0.03262i
% 
% p =
%   -0.90000 
%   -0.27812 - 0.85595i
%   -0.27812 + 0.85595i
%    0.72812 - 0.52901i
%    0.72812 + 0.52901i
% 
% f = [](0x0)



Subsections
Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``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
CCRMA