On the optimality of the classical stability criteria for 1-D and 2-D digital recursive filters

  • Authors:

  • M. Barret;M. Benidir

  • Affiliations:

  • Supélec, Établissement de Metz, Metz, France;Université de Paris-Sud, Gif-sur-Yvette, France

  • Venue:
  • ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: digital speech processing - Volume III
  • Year:
  • 1993

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Abstract

A bound for the complexity of any algebraic criterion, giving necessary and sufficient conditions for the stability of digital recursive filters is proposed, in 1-D and 2-D cases. For this, we show that the set of the 1-D Schur polynomials with a degree not greater than n, in the (n+1)-dimensional space of the polynomial coefficients, is connex and its boundary is a hypedace which has an irreducible equation.