residue (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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Owning Class: polynomials

Requires: MathScript RT Module

Syntax

[b, a] = residue(r, p, k)

[r2, p2, k2] = residue(b2, a2)

Description

Computes the partial fraction expansion of two polynomials or transforms a given partial fraction expansion into the original polynomial representation.

Details

Examples

Inputs

Name Description
r Specifies the residues of the partial fraction expansion. r is a real or complex vector.
p Specifies the poles of the partial fraction expansion. p is a real or complex vector.
k Specifies the coefficients in descending order of power of the quotient polynomial of a and b.
b2 Specifies the coefficients in descending order of power of the numerator polynomial.
a2 Specifies the coefficients in descending order of power of the denominator polynomial.

Outputs

Name Description
b Returns the coefficients in descending order of power of the numerator polynomial.
a Returns the coefficients in descending order of power of the denominator polynomial.
r2 Returns the residues of the partial fraction expansion. r2 is a real or complex vector.
p2 Returns the poles of the partial fraction expansion. p2 is a real or complex vector.
k2 Returns the coefficients in descending order of power of the quotient polynomial of a2 and b2.

Details

LabVIEW computes a and b using the following equation if no multiple roots exist:
bs/as = (r1/(s-p1)) + (r2/(s-p2)) + ... + (rn/(s-pn)) + ks
where s is the power and n is the number of elements in the partial fraction expansion.

If multiple poles exist, that is, if pj = ... = pj+m-1 where j is the element index and m is the multiple, then the partial fraction expansion includes the following terms: (rj/(s-pj)) + (rj+1/(s-pj))2 + ... + (rj+m-1/(s-pj))m.

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

Examples

B = [1, 2, 3, 4]
A = [1, 1]
[R, P, K] = residue(B, A)