The Computer Implementation of Bilinear s-z Transformation Using New Continued Fraction Algorithms

Mohammed Ismail, Hamid Vakilzadian

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The application of continued fractions to the bilinear transformation of polynomials is introduced. The operations to perform the transformation are continued fraction expansion in the s domain and continued fraction inversion in the z domain. Novel algorithms and computer programs to implement the expansion and the inversion are presented. In particular, the expansion algorithm provides closed forms for the continued fraction quotients in terms of the corresponding rational function coefficients. It is shown that the computer implementation of this algorithm iteratively results in a simple procedure for evaluating the quotients by hand and saves considerable computation time. It is especially noted that the algorithmic character of continued fractions leads to simple systematic computation scheme. The proposed method of bilinear transformation capitalizes on the knowledge gained in continuous-time stability theory and introduces the more recent topic of z-domain continued fractions and their applications. Numerical examples and computer data are provided. The paper brings together contributions in the modern areas of s- and z-domain system theory, as well as algorithm development for computer implementation, and attempts to close the gaps between new research results and their introduction in a classroom environment.

Original languageEnglish (US)
Pages (from-to)270-279
Number of pages10
JournalIEEE Transactions on Education
Issue number3
StatePublished - Aug 1989

ASJC Scopus subject areas

  • Education
  • Electrical and Electronic Engineering


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