residuez: Z-transform partial fraction expansion

In gsignal: Signal Processing

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, [e-mail].
Conversion to R by Geert van Boxtel, [e-mail]

See Also

residue, residued

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 documentation built on Sept. 12, 2024, 6:27 a.m.