Software for Partial Fraction Expansion

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Software for Partial Fraction Expansion

Figure 6.3 illustrates the use of residuez (§J.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 .
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)

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

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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
    Transfer Function Analysis
       Partial Fraction Expansion
          Software for Partial Fraction Expansion