Exact convergence analysis of adaptive filter algorithms without persistently exciting condition

Author

Sakai, Hideaki

Author_Institution

Dept. of Syst. Sci., Kyoto Univ., Japan

Volume

3

fYear

2005

fDate

28 Aug.-2 Sept. 2005

Abstract

Exact convergence analysis of the RLS and LMS algorithms in adaptive filtering is presented for the case of sinusoidal signal cancellation without the persistently exciting condition. This situation occurs when the number of tap coefficients of adaptive filter exceeds that of the complex sinusoids in the input signal. The convergent point of both algorithms is shown to be the one determined by the pseudo inverse of the deterministic covariance matrix. The convergence proof for the LMS algorithm is based on the Lyapunov function method.

Keywords

Lyapunov matrix equations; adaptive filters; convergence; covariance matrices; least mean squares methods; network analysis; LMS algorithms; Lyapunov function method; RLS algorithm; adaptive filter algorithm; complex sinusoid; deterministic covariance matrix; exact convergence analysis; persistently exciting condition; sinusoidal signal cancellation; tap coefficient; Adaptive filters; Algorithm design and analysis; Convergence; Filtering algorithms; Finite impulse response filter; Frequency; Least squares approximation; Noise cancellation; Resonance light scattering; Signal processing algorithms;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuit Theory and Design, 2005. Proceedings of the 2005 European Conference on

Print_ISBN

0-7803-9066-0

Type

conf

DOI

10.1109/ECCTD.2005.1523108

Filename

1523108