Modified Prony Method with Amplitude-Phase Correction

To approximate discrete non-causal deterministic signals, a new modification of the Prony method with amplitude-phase correction (APC) is proposed, which makes it possible to remove a number of restrictions on the signal and improve the quality of its approximation. This is achieved by switching to a two-component non-causal Prony model and adding a special signal to its structure that corrects the amplitude-phase characteristics of the model. A method is developed for optimal estimation of the parameters of the proposed modified APC model, based on a known finite set of signal samples. On its basis, we obtain strict analytical expressions describing the algorithm for approximating a discrete non-causal signal and expressions for its complex and amplitude spectra. The proposed approximation method and the well-known Prony method are compared experimentally. It is shown that the use of the modified Prony method with amplitude-phase correction allows, with the same order of the model, to significantly reduce the signal approximation errors in the time and spectral domains and thereby expand the area of its practical application.