Stability Test for Two-Dimensional Recursive Filters

Brian D.O. Anderson; Eliahu I. Jury

doi:10.1109/TAU.1973.1162491

Stability Test for Two-Dimensional Recursive Filters

Brian D.O. Anderson, Eliahu I. Jury

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

83 Citations (Scopus)

Abstract

For deciding the stability of a two-dimensional filter, it is of interest to determine whether or not a prescribed polynomial in the variables Z1 and z2 is nonzero in the region |Z1| < 1 ∩ |z2| < 1. A new procedure for testing for this property is given, which does not involve the use of bilinear tranformations. Key parts of the test involve the construction of a Schur-Cohn matrix and the checking for positivity on the unit circle of a set of self-inversive polynomials.

Original language	English
Pages (from-to)	366-372
Number of pages	7
Journal	IEEE Transactions on Audio and Electroacoustics
Volume	21
Issue number	4
DOIs	https://doi.org/10.1109/TAU.1973.1162491
Publication status	Published - Aug 1973
Externally published	Yes

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10.1109/TAU.1973.1162491

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abstract = "For deciding the stability of a two-dimensional filter, it is of interest to determine whether or not a prescribed polynomial in the variables Z1 and z2 is nonzero in the region |Z1| < 1 ∩ |z2| < 1. A new procedure for testing for this property is given, which does not involve the use of bilinear tranformations. Key parts of the test involve the construction of a Schur-Cohn matrix and the checking for positivity on the unit circle of a set of self-inversive polynomials.",

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AB - For deciding the stability of a two-dimensional filter, it is of interest to determine whether or not a prescribed polynomial in the variables Z1 and z2 is nonzero in the region |Z1| < 1 ∩ |z2| < 1. A new procedure for testing for this property is given, which does not involve the use of bilinear tranformations. Key parts of the test involve the construction of a Schur-Cohn matrix and the checking for positivity on the unit circle of a set of self-inversive polynomials.

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Stability Test for Two-Dimensional Recursive Filters

Abstract

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