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On orthogonal realizations for adaptive IIR filters
Author(s) -
Cousseau J.,
Diniz P. S. R.,
Sentoni G.,
Agameni O.
Publication year - 2000
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/1097-007x(200009/10)28:5<481::aid-cta120>3.0.co;2-r
Subject(s) - infinite impulse response , realization (probability) , orthonormal basis , adaptive filter , finite impulse response , mathematics , control theory (sociology) , algorithm , minimal realization , convergence (economics) , orthonormality , computer science , filter (signal processing) , digital filter , linear system , artificial intelligence , mathematical analysis , control (management) , statistics , physics , quantum mechanics , economics , computer vision , economic growth
Convergence speed is one of the main concerns in adaptive IIR filters. Fast convergence can be closely related to adaptive filter realization. However, with the exception of the lattice realization that is based on the nice properties of Szëgo orthonormal polynomials, no other adaptive IIR filter realization using orthonormal characteristics seems to be extensively studied in the literature. Furthermore, many orthogonal realizations for adaptive FIR filters, that are particularly suitable for rational modelling, have been proposed in the past years. Since rational orthogonal basis functions are a powerful tool for efficient system representation they seem attractive for adaptive IIR filters. In this paper, we present some theoretical results related to the properties of a generalized orthonormal realization when used for mean‐square output error minimization in a system identification application. One result is related to the low computational complexity of the updating gradient algorithm when some properties of the orthonormal realization are used. An additional result establishes conditions for the stationary points of the proposed updating algorithm. In order to confirm the expected performance of the new realization, some simulations and comparisons with competing realizations in terms of computational complexity and convergence speed are presented. Copyright © 2000 John Wiley & Sons, Ltd.