Geodesic
Stability of Weighted Darma Filters
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 49-64

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1998-009-1
Mots-clés : 47A62, 47B37, 93D25, 42A85, 47N70, Difference equations, adaptive DARMA filters, weighted shifts, stability and boundedness, automatic continuity 
Harrison, K. J.; Ward, J. A.; Eaton, L-J. Stability of Weighted Darma Filters. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 49-64. doi: 10.4153/CMB-1998-009-1
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[1] 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] 2. Kailath, T., Linear Systems. Prentice-Hall, 1980. Google Scholar

[3] 3. Ramsey, L. T., Best bounds for the stability of DARMA filters with constant coefficients. SIAM Rev. 31 (1989), 365–400. Google Scholar

[4] 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] 5. Ramsey, L. T. and Sollervall, H., Personal communication. Google Scholar

[6] 6. Shields, A. L., Weighted shift operators and analytic function theory. Math. Surveys 13 (1974), 49–128. Google Scholar

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