A Very Simple Method of Finding the Residues at Repeated Poles of a Rational Function in z−1

  • Suhash Chandra Dutta Roy

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 −1. 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.


Partial fraction expansion Repeated poles New method 


  1. 1.
    S.C. Dutta Roy, Comments on fair and square computation of inverse z-transforms of rational functions. IEEE Trans. Educ. 58(1), 56–57 (Feb 2015)Google Scholar
  2. 2.
    S.C. Dutta Roy, Carry out partial fraction expansion of rational functions with multiple poles—without tears. Stud. J. IETE. 26, 129–31 (Oct 1985)Google Scholar
  3. 3.
    F.F. Kuo, in Network Analysis and Synthesis (Wiley, New York, 1966), pp. 153–154Google Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology DelhiNew DelhiIndia

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