A procedure for calculating the best exponents for signal representation

Abstract

The approximation of a given signal over (0,^ ) by a linear combination of a given number n of exponentials in such a sense that the integrated squared error is minimized over both the coefficients of the linear combination and the exponents used is discussed. The necessary conditions for the minimizations lead to nonlinear equations. Analog and digital computer implementations have been developed that are capable of adjusting the exponents of the basis functions and the coefficients of the linear combinations to minimize the integrated squared error between a signal and its representation. The influence of each parameter of the orthonormal filters on the performance criterion is determined using an iterative convergent process. These parameter changes are introduced into the analog and digital systems to form a closed loop system.