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Existence of stationary points for reduced-order hyperstable adaptive IIR filters

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3 Author(s)
Regalia, P.A. ; Dept. Signal et Image, Inst. Nat. des Telecommun., Evry, France ; Mboup, M. ; Ashari, M.

We establish the existence of asymptotic stationary points for a class of adaptive IIR filtering algorithms, including (S)HARF, the Feintuch (1996) algorithm, and Landau's (1976) algorithm, for reduced-order cases. We show first that the nonlinear equations characterizing a stationary point admit a solution giving rise to a stable transfer function, when the input is white noise. We then show that an analytic procedure to construct the solution may be reduced to the Nevanlinna-Pick interpolation problem. The white noise assumption on the input simplifies the mathematics of an already difficult problem, although the existence proof appears extendable to correlated inputs as well

Published in:

Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on  (Volume:5 )

Date of Conference:

21-24 Apr 1997