Parametric least squares approximation using gamma bases

Author

Çelebi, Samel ; Principe, Jose C.

Author_Institution

Comput. NeuroEng. Lab., Florida Univ., Gainesville, FL, USA

Volume

43

Issue

3

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

781

Lastpage

784

Abstract

We study the problem of linear approximation of a signal using the parametric gamma bases in L² space. These bases have a time scale parameter, which has the effect of modifying the relative angle between the signal and the projection space, thereby yielding an extra degree of freedom in the approximation. Gamma bases have a simple analog implementation that is a cascade of identical lowpass filters. We derive the normal equation for the optimum value of the time scale parameter and decouple it from that of the basis weights. Using statistical signal processing tools, we further develop a numerical method for estimating the optimum time scale

Keywords

cascade networks; filtering theory; least squares approximations; low-pass filters; parameter estimation; signal representation; statistical analysis; analog implementation; basis weights; gamma bases; linear signal approximation; lowpass filters; moment matching; numerical method; optimum time scale; parametric least squares approximation; projection space; signal representation; statistical signal processing tools; time scale parameter; Adaptive filters; Artificial neural networks; Digital filters; Echo cancellers; Finite impulse response filter; Frequency; Intelligent networks; Least squares approximation; Linear approximation; Transfer functions;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.370635

Filename

370635