Frequency-domain bias decomposition for LMS and LS adaptive filters

Authors:
Gernot Kubin;C. Richard Johnson, Jr.;Bo Egardt
Affiliations:
Vienna University of Technology, Vienna, Austria;School of Electrical Engineering, Cornell University, Ithaca, NY;Control Engineering Laboratory, Chalmers Univ. of Technology, Göteborg, Sweden
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: digital speech processing - Volume III
Year:
1993

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Adaptation and tracking in system identification—a survey

Automatica (Journal of IFAC) - Identification and system parameter estimation

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Abstract

Frequency domain descriptions of dynamic system performance are widely utilized in signal processing systems analysis and design. Curiously, frequency domain descriptions of adaptive filter performance are rare. This weak link to a widely exploited engineering tool motivates consideration of a fundamental re-evaluation of adaptive filter performance, and subsequent design rules, in frequency domain terms. In this contribution we present the frequency-domain analysis for the bias distribution in a reduced-order modeling experiment using either LMS or LS-type algorithms. We develop and prove a new theorem that allows the exact decomposition of the bias into a sum of components related to the eigenfilters of the input autocorrelation matrix.