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Numerically, the partial fraction expansion of a ratio of polynomials represents an ill-posed problem. If the denominator polynomial, a s , is near a polynomial with multiple roots, then small changes in the data, including roundoff errors, can result in arbitrarily large changes in the resulting poles and residues.

Problem formulations making use of state-space or zero-pole representations are preferable. Digital Signal Processing. Prentice-Hall, , p. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location.

Toggle Main Navigation. Search MathWorks. Open Mobile Search. Off-Canvas Navigation Menu Toggle. Main Content. Open Live Script. Input Arguments collapse all b — Coefficients of numerator polynomial vector of numbers. Output Arguments collapse all r — Residues of partial fraction expansion column vector of numbers. Residues of partial fraction expansion, returned as a column vector of numbers. Poles of partial fraction expansion, returned as a column vector of numbers.

Algorithms residue first obtains the poles using roots. References [1] Oppenheim, A. You have a modified version of this example. Problem formulations making use of state-space or zero-pole representations are preferable. Examples If the ratio of two polynomials is expressed as. Now, convert the partial fraction expansion back to polynomial coefficients. Note that the result is normalized for the leading coefficient in the denominator. See Also deconv , poly , roots.

References [1] Oppenheim, A. Vectors that specify the coefficients of the polynomials in descending powers of. Algorithm It first obtains the poles with roots.

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