residue: Partial fraction expansion

In gsignal: Signal Processing

Partial fraction expansion

Description

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

Usage

residue(b, a, tol = 0.001)

rresidue(r, p, k, tol = 0.001)

Arguments

b	coefficients of numerator polynomial
a	coefficients of denominator polynomial
tol	tolerance. Default: 0.001
r	residues of partial fraction expansion
p	poles of partial fraction expansion
k	direct term

Details

The call res <- residue(b, a) computes the partial fraction expansion for the quotient of the polynomials, b and a.

The call res <- rresidue(r, p, k) performs the inverse operation and computes the reconstituted quotient of polynomials, b(s) / a(s), from the partial fraction expansion; represented by the residues, poles, and a direct polynomial specified by r, p and k, and the pole multiplicity e.

Value

For residue, a list containing r, p and k. For rresidue, a list containing b and a.

Author(s)

Tony Richardson, [e-mail],
Ben Abbott, [e-mail],
adapted by John W. Eaton.
Conversion to R by Geert van Boxtel, [e-mail]

Examples

b <- c(-4, 8)
a <- c(1, 6, 8)
rpk <- residue(b, a)
ba <- rresidue(rpk$r, rpk$p, rpk$k)

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