residuez function

Z-transform partial fraction expansion

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

residuez(b, a)

Arguments

• b: coefficients of numerator polynomial
• a: coefficients of denominator polynomial

Returns

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))

Details

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

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)

See Also

residue, residued

Author(s)

Julius O. Smith III, jos@ccrma.stanford.edu .

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com