Modification of the Prony Method for Pulse Signal Modeling

This paper considers a modification of the Prony parametric approximation method for modeling impulse signals. It is assumed that the experimentally measured signal is represented as a time series. The method is based on the construction of a model of the experimental signal under study as a sum of damped sinusoids. The problem, which does not allow approximating impulse signals with the required accuracy, is revealed. On the basis of the analysis of the classical formulation of the method, its modification is proposed, which allows to solve this problem. Mathematical substantiation of the modified method is presented. The possibility of interference filtering on the basis of analyzing the spectral structure of the signal model is substantiated. The possibility of identification of dynamic characteristics of elements of automatic control systems in analytical form using the developed approach is investigated. The results of modeling a test signal in the form of a rectangular pulse are given. The directions of development of the modified method are discussed, as well as possible areas of practical application.