Modified Proni Method with a Correctional Control Signal
DOI:
https://doi.org/10.52575/2687-0932-2023-50-3-712-730Keywords:
signal approximation, Prony method, recursive model, difference equations, discrete signals, causal signals, non-causal signalsAbstract
To approximate discrete non-causal signals given on an infinite two-sided time interval, a two-component modification of the Prony model is proposed, in which one component approximates the causal part of the signal, and the other, the anti-causal part. To reduce the approximation errors arising from the restrictions on the multiplicity of the poles, a special corrective signal is added to each component of the exponential Prony model, which plays the role of the optimal control and leads to its amplitude-phase correction. A method for optimal estimation of the parameters of the proposed two-component Prony model is developed and, on its basis, analytical expressions are obtained for the algorithm of the best approximation of signals by its finite sample of samples according to the minimum squared error (MSE) criterion. Strict analytical expressions are obtained for the spectrum of the approximating signal, built on the basis of the proposed Prony method with a corrective control signal. The results of a comparative experiment are presented, confirming the good quality of the signal approximation in both the time and spectral domains under the conditions of the multiplicity of the poles. It is shown that in this case the proposed method makes it possible to reduce the approximation errors by more than 80 times compared to the conventional Prony method.
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