Title :
Parametric least squares approximation using gamma bases
Author :
Çelebi, Samel ; Principe, Jose C.
Author_Institution :
Comput. NeuroEng. Lab., Florida Univ., Gainesville, FL, USA
fDate :
3/1/1995 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
