Abstract
A method for approximation of an arbitrary continuous function in the neighborhood of a given point by complex exponential functions (exponentials) is described. The method is similar to the Taylor series to the effect that approximation is performed by the derivatives at the given point. Determination of parameters of the exponentials is made on the basis of a modified Prony’s method. It is shown that the method makes it possible to simulate the local behavior of periodic and quasiperiodic processes more effectively than a Taylor series. An algorithm for estimating the instantaneous parameters of the single-component quasiperiodic continuous signals is obtained. The relation to a known energy separation algorithm (ESA) is shown. A separate algorithm for discrete signals by using finite differences is obtained. The applicability of the algorithm for practical analysis of discrete signals with consideration of the influence of additive noise on the accuracy of the parameter estimates is investigated. Experimental comparison of the algorithm with the known methods of estimating instantaneous parameters on the basis of the Prony’s method and ESA is performed.
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Original Russian Text © E.S. Azarov, M.I. Vashkevich, A.A. Petrovsky, 2015, published in Avtomatika i Vychislitel’naya Tekhnika, 2015, No. 2, pp. 65–80.
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Azarov, E.S., Vashkevich, M.I. & Petrovsky, A.A. Estimation of the instantaneous signal parameters using a modified Prony’s method. Aut. Control Comp. Sci. 49, 110–121 (2015). https://doi.org/10.3103/S0146411615020029
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DOI: https://doi.org/10.3103/S0146411615020029