If you have followed the last chapter carefully, this one would be a cakewalk! The two discussions are similar except for the variables. A very simple method is given for finding the residues at repeated poles of a rational function in z ā1. Compared to the multiple differentiation formula given in most textbooks, and several other alternatives, this method appears to be the simplest and the most elegant. It requires only a long division preceded by a small amount of processing of the given function.
Source: S. C. Dutta Roy, āA Very Simple Method of Finding the Residues at Repeated Poles of a Rational Function in zā1,ā IETE Journal of Education, vol. 56, pp 68ā70, JulyāDecember 2015.
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References
S.C. Dutta Roy, Comments on fair and square computation of inverse z-transforms of rational functions. IEEE Trans. Educ. 58(1), 56ā57 (Feb 2015)
S.C. Dutta Roy, Carry out partial fraction expansion of rational functions with multiple polesāwithout tears. Stud. J. IETE. 26, 129ā31 (Oct 1985)
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Dutta Roy, S.C. (2018). A Very Simple Method of Finding the Residues at Repeated Poles of a Rational Function in zā1 . In: Circuits, Systems and Signal Processing. Springer, Singapore. https://doi.org/10.1007/978-981-10-6919-2_6
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