On the Necessity of Estimating the Transfer Level in an Allpass-FIR ADF by the Use of Lyapunov Criteria

Shin'ichi ARITA
Yoshio ITOH
Yutaka FUKUI

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A    No.5    pp.888-894
Publication Date: 2000/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
allpass filter,  transfer level,  Lyapunov criteria,  

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In this paper we present an analysis based on the indirect Lyapunov criteria, that is used to study the convergence of an infinite impulse response (IIR) adaptive digital filter (ADF) based on estimation of the allpass system. The analysis is then extended to investigate the necessity of directly estimating the transfer level of the unknown system. We consider two cases of modeling the ADF. In the first system, the allpass section of the ADF estimates only the real poles of the unknown system while in the second system, both real and complex poles the allpass section are estimated. From the analysis and computer simulation, we realize that the poles of the ADF converge selectively to the poles of the unknown system, depending on the sign of the step size of adaptation. Using these results we proposed a new method to control the convergence of the poles the IIR ADF based on estimation of the allpass system.