Comparative analysis of accuracy in evaluating poles of frequency characteristics by methods of fractional-rational approximation

Mikhail Andreev; Oleg Drobakhin; Maksim Potapov

doi:10.3103/S0735272724110025

Authors

Mikhail Andreev Oles Honchar Dnipro National University, Dnipro, Ukraine https://orcid.org/0000-0001-7360-8058
Oleg Drobakhin Oles Honchar Dnipro National University, Dnipro, Ukraine https://orcid.org/0009-0006-9738-4515
Maksim Potapov Oles Honchar Dnipro National University, Dnipro, Ukraine https://orcid.org/0009-0002-9060-191X

DOI:

https://doi.org/10.3103/S0735272724110025

Keywords:

fractional-rational model, Cauchy method, quasi-solution method, chain fraction method, adaptive Antulas-Anderson method, AAA, vector fitting method, resolution, pole estimation accuracy

Abstract

A comparative analysis of the accuracy and robustness of pole estimates when approximating relationships using a fractional rational model is presented. The results are obtained through numerical simulation for several models, including single-pole, pole-zero, and two-pole models. The resolution in estimating the values of closely spaced poles has been investigated using a two-pole model. The methods considered included the quasi-solution method, the Cauchy method, the chain fraction method, vector fitting, and the adaptive Antulas–Anderson (AAA) method. An iterative version of the Cauchy method is proposed, which exhibits superior characteristics compared to the known version. The iterative version of the Cauchy method, the chain fraction method, and the quasi-solution method provide high robustness and accuracy of estimates among all considered models, surpassing other methods. The above-specified three methods are a convenient tool for investigating the poles of the characteristics of various electrodynamic structures and frequency-selective structures, in particular filters.

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