Wavelet transform based adaptive filters: analysis and new results

Author

Erdol, Nurgun ; Basbug, Filiz

Author_Institution

Dept. of Electr. Eng., Florida Atlantic Univ., Boca Raton, FL, USA

Volume

44

Issue

9

fYear

1996

fDate

9/1/1996 12:00:00 AM

Firstpage

2163

Lastpage

2171

Abstract

In this paper the wavelet transform is used in an adaptive filtering structure. The coefficients of the adaptive filter are updated by the help of the least mean square (LMS) algorithm. First, the wavelet transform based adaptive filter (WTAF) is described and it is analyzed for its Wiener optimal solution. Then the performance of the WTAF is studied by the help of learning curves for three different convergence factors: (1) constant convergence factor, (2) time-varying convergence factor, and (3) exponentially weighted convergence factor. The exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation. It is shown for two different sets of data that the rate of convergence increases significantly for all three WTAF structures as compared to that of time-domain LMS. The high convergence rates of the WTAF give us reason to expect that it will perform well in tracking rapid changes in a signal

Keywords

Wiener filters; adaptive filters; convergence of numerical methods; digital filters; least mean squares methods; tracking filters; wavelet transforms; WTAF structures; Wiener optimal solution; constant convergence factor; convergence; exponentially weighted convergence factor; learning curves; least mean square; scale-based variation; time-varying convergence factor; tracking; wavelet transform based adaptive filters; weight update equation; Adaptive filters; Continuous wavelet transforms; Convergence; Discrete wavelet transforms; Equations; Least squares approximation; Signal analysis; Time domain analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.536674

Filename

536674