Z-DOMAIN CONTINUED FRACTION EXPANSIONS FOR STABLE DISCRETE SYSTEMS POLYNOMIALS.

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Abstract

A z-plane continued fraction expansion (CFE) that is related to the first Cauer s-plane CFE via Bruton's (1975) LDI transformation is considered. Necessary and sufficient conditions are imposed on the CFE for a polynomial to be stable (have all its zeros inside the z-plane unit circle). The implementation of this CFE in a tabular form establishes the Routh-like stability table first derived by the author (1983). The application of this stability table is now extended to also count zeros outside the unit circle. However, the closer analogy of the present formulation to the s-plane Cauer CFEs and Routh table suggest additional merits of this formulation to the design of digital networks (e. g. , switched-capacitor filters). A brief account of three related alternative CFEs is included.

Original languageEnglish
Pages (from-to)1162-1166
Number of pages5
JournalIEEE Transactions on Circuits and Systems
VolumeCAS-32
Issue number11
DOIs
StatePublished - 1985

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