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

Yuval Bistritz

doi:10.1109/tcs.1985.1085629

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

Yuval Bistritz^*

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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 language	English
Pages (from-to)	1162-1166
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems
Volume	CAS-32
Issue number	11
DOIs	https://doi.org/10.1109/tcs.1985.1085629
State	Published - 1985

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title = "Z-DOMAIN CONTINUED FRACTION EXPANSIONS FOR STABLE DISCRETE SYSTEMS POLYNOMIALS.",

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.",

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AB - 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.

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

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