residued function

delayed z-transform partial fraction expansion

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

residued(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

In the usual PFE function residuez, the IIR part (poles p and residues r) is driven in parallel with the FIR part (f). In this variant, the IIR part is driven by the output of the FIR part. This structure can be more accurate in signal modeling applications.

Examples

b <- c(2, 6, 6, 2)
a <- c(1, -2, 1)
resd <- residued(b, a)
resz <- residuez(b, a)

References

https://ccrma.stanford.edu/~jos/filters/residued.html

See Also

residue, residuez

Author(s)

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

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