Linear System Approximation by Differential Analyzer Simulation of Orthonormal Approximation Functions

Various analytic procedures have been proposed for minimum integral-square-error approximation of prescribed linear systems; however, they often involve computational difficulties. In the procedure developed in this paper, a group of N linear approximating systems with orthonormal impulse responses ¿n(t) are realized by operational amplifier circuits. When h(-t) forces the systems (h(t) is the impulse response of the prescribed system) it is found that their outputs at t = 0 are an, the coefficients in {see the Equation in PDF File} the approximate impulse response. The following points relative to the approximation procedure are developed: constrained and weighted integral-square-error approximations, derivation and realization of orthonormal functions, physical realization of h*(t), evaluation of error h(t)-h*(t), and analysis of computer errors. Several approximation examples are given.