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Stability of Weighted Darma Filters

Published online by Cambridge University Press:  20 November 2018

K. J. Harrison ,
J. A. Ward  and
L-J. Eaton
K. J. Harrison
Affiliation:
Department of Mathematics and Statistics Murdoch University Murdoch, WA 6150 Australia, e-mail: harrison@prodigal.murdoch.edu.au
J. A. Ward
Affiliation:
Department of Mathematics and Statistics Murdoch University Murdoch, WA 6150 Australia, e-mail: ward@prodigal.murdoch.edu.au
L-J. Eaton
Affiliation:
Department of Mathematics and Statistics University of Canterbury Christchurch New Zealand, e-mail: L.Eaton@math.canterbury.ac.nz
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Abstract

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We study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case.

Keywords

47A6247B3793D2542A8547N70Difference equationsadaptive DARMA filtersweighted shiftsstability and boundednessautomatic continuity

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 49 - 64
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Harrison, K. J., Eaton, L-J., and Ward, J. A., Automatic continuity of perturbations of causal operators. Bull. Austral. Math. Soc. 55 (1997), 281–291.Google Scholar
2. Kailath, T., Linear Systems. Prentice-Hall, 1980.Google Scholar
3. Ramsey, L. T., Best bounds for the stability of DARMA filters with constant coefficients. SIAM Rev. 31 (1989), 365–400.Google Scholar
4. Ramsey, L. T., Stability of (Deterministic) Adaptive Auto-regressive Filters. Proc. St. Lawrence Univ. Conf. on Harmonic Analysis, Contemp. Math. 91 (1987), 217–246.Google Scholar
5. Ramsey, L. T. and Sollervall, H., Personal communication.Google Scholar
6. Shields, A. L., Weighted shift operators and analytic function theory. Math. Surveys 13 (1974), 49–128.Google Scholar