Exact Convergence Analysis of Adaptive Filter Algorithms Without the Persistently Exciting Condition

Author

Sakai, Hideaki ; Yang, Jun-Mei ; Oka, Tetsuya

Author_Institution

Dept. of Syst. Sci., Kyoto Univ.

Volume

55

Issue

5

fYear

2007

fDate

5/1/2007 12:00:00 AM

Firstpage

2077

Lastpage

2083

Abstract

Exact convergence analysis of the recursive least square and least mean square (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 the 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. Finally, the validity of the obtained results is supported by simulation results

Keywords

adaptive filters; covariance matrices; least squares approximations; Lyapunov function method; adaptive filter algorithms; covariance matrix; least mean square algorithms; pseudo inverse; recursive least square algorithms; sinusoidal signal cancellation; Adaptive filters; Algorithm design and analysis; Convergence; Finite impulse response filter; Frequency; Least squares approximation; Least squares methods; Noise cancellation; Resonance light scattering; Signal processing algorithms; Adaptive filter algorithms; exact convergence analysis; persistently exciting condition; sinusoidal noise cancellation;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2006.890930

Filename

4156425