Parametric least squares approximation using gamma bases

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 which 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. EDICS NO: SP 2.3.1 Correspondence : Jose C. Principe Address : Computational Neuroengineering Laboratory CSE 447 University of Florida Gainesville FL32611 Phone : (904) 392-2662 Fax : (904) 392-0044 E-Mail : [email protected]