Parametric least squares approximation using gamma bases

We study the problem of linear approximation of a signal using the parametric gamma bases in L/sup 2/ 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.<
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