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residuez

Z-transform partial fraction expansion


Description

Finds the residues, poles, and direct term of a Partial Fraction Expansion of the ratio of two polynomials.

Usage

residuez(b, a)

Arguments

b

coefficients of numerator polynomial

a

coefficients of denominator polynomial

Details

residuez converts a discrete time system, expressed as the ratio of two polynomials, to partial fraction expansion, or residue, form.

Value

A list containing

r

vector of filter pole residues of the partial fraction

p

vector of partial fraction poles

k

vector containing FIR part, if any (empty if length(b) < length(a))

Author(s)

Julius O. Smith III, jos@ccrma.stanford.edu.
Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com

See Also

Examples

b0 <- 0.05634
b1 <- c(1,  1)
b2 <- c(1, -1.0166, 1)
a1 <- c(1, -0.683)
a2 <- c(1, -1.4461, 0.7957)
b <- b0 * conv(b1, b2)
a <- conv(a1, a2)
res <- residuez(b, a)

gsignal

Signal Processing

v0.3-1
GPL-3
Authors
Geert van Boxtel [aut, cre] (Maintainer), Tom Short [aut] (Author of 'signal' package), Paul Kienzle [aut] (Majority of the original sources), Ben Abbott [ctb], Juan Aguado [ctb], Muthiah Annamalai [ctb], Leonardo Araujo [ctb], William Asquith [ctb], David Bateman [ctb], David Billinghurst [ctb], Juan Pablo Carbajal [ctb], André Carezia [ctb], Vincent Cautaerts [ctb], Eric Chassande-Mottin [ctb], Luca Citi [ctb], Dave Cogdell [ctb], Carlo de Falco [ctb], Carne Draug [ctb], Pascal Dupuis [ctb], John W. Eaton [ctb], R.G.H Eschauzier [ctb], Andrew Fitting [ctb], Alan J. Greenberger [ctb], Mike Gross [ctb], Daniel Gunyan [ctb], Kai Habel [ctb], Kurt Hornik [ctb], Jake Janovetz [ctb], Alexander Klein [ctb], Peter V. Lanspeary [ctb], Bill Lash [ctb], Friedrich Leissh [ctb], Laurent S. Mazet [ctb], Mike Miller [ctb], Petr Mikulik [ctb], Paolo Neis [ctb], Georgios Ouzounis [ctb], Sylvain Pelissier [ctb], Francesco Potortì [ctb], Charles Praplan [ctb], Lukas F. Reichlin [ctb], Tony Richardson [ctb], Asbjorn Sabo [ctb], Thomas Sailer [ctb], Rolf Schirmacher [ctb], Rolf Schirmacher [ctb], Ivan Selesnick [ctb], Julius O. Smith III [ctb], Peter L. Soendergaard [ctb], Quentin Spencer [ctb], Doug Stewart [ctb], P. Sudeepam [ctb], Stefan van der Walt [ctb], Andreas Weber [ctb], P. Sudeepam [ctb], Andreas Weingessel [ctb]
Initial release
2021-05-02

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