Skip to main content
SpringerLink
Log in

A set of necessary stability conditions form-D nonlinear digital filters

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper addresses the problem of global asymptotic stability in recursive first hyperquadrant causalm-D digital filters. A set of simple-to-check 1-D conditions necessary for stability of them-D system is given. Generalizations tov-dimensional (v<m) subsystems are also provided. These derived conditions are useful in determining asymptotic convergence ofm-D digital filters implemented in fixed or floating point arithmetic. The set of 1-D conditions can be considered the analogous result to practical bounded input bounded output (BIBO) stability for linearm-D systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T.T. Aboulnasr and M.M. Fahmy, Finite word-length effects in two-dimensional digital filters, inMulti-dimensional Systems: Techniques and Applications, S.G. Tzafestas, ed., Marcel Dekker, New York, March 1986.

    Google Scholar 

  2. P. Agathoklis and L.T. Bruton, Practical BIBO-stability of N-dimensional discrete systems,1983 IEEE International Symposium on Circuits and Systems, Newport Beach, CA 1983.

  3. P. Bauer, Finite wordlength effects inm -D digital filters with singularities on the stability boundary,IEEE Trans. on Signal Processing, Vol. 40, No. 4, pp. 894–900, April 1992.

    Google Scholar 

  4. P. Bauer and E.I. Jury, Stability conditions for multi-dimensional digital state space filters under finite wordlength effects,IEEE Trans. on Acoustic, Signal, and Speech Processing, Vol. 38, No. 9, pp. 1578–1587, 1990.

    Google Scholar 

  5. T. Bose and M.Q. Chen, Stability of digital filters implemented with two's complement truncation quantization,IEEE Transactions on Signal Processing, Vol. SP-40, pp. 24–31, Jan. 1992.

    Google Scholar 

  6. T. Bose and D.A. Trautman, Two's complement quantization in two-dimensional state space digital filters,IEEE Transactions on Signal Processing, Vol. SP-40, Oct. 1992.

  7. W.S. Lu and A. Antoniou,Two-Dimensional Digital Filters, Marcel Dekker, New York, 1992.

    Google Scholar 

  8. S. G. Tzafestas, A. Kanellakis, and N. J. Theodorou, Two-dimensional digital filters without overflow oscillations and instability due to finite wordlength,IEEE Trans. on Signal Processing, Vol. 40, No. 9, pp. 2311–2317, Sept. 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Laboratory of Image and Signal Analysis, University of Notre Dame, 46556, Notre Dame, IN

    Peter H. Bauer

Authors
  1. Peter H. Bauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bauer, P.H. A set of necessary stability conditions form-D nonlinear digital filters. Circuits Systems and Signal Process 14, 555–561 (1995). https://doi.org/10.1007/BF01260337

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01260337

Keywords

Search

Navigation