A prony method variant which surpasses the Adaptive LMS filter in the output signal's representation of input

TL;DR

This paper introduces an improved Prony method variant that enhances signal approximation accuracy over the Adaptive LMS filter by adjusting for computational errors during the initial autoregressive modeling step.

Contribution

The study proposes a novel modification to the Prony method that accounts for computational errors, resulting in more precise signal representations than the Adaptive LMS filter.

Findings

The modified Prony method achieves higher precision in signal approximation.

It demonstrates more consistent results compared to the Adaptive LMS filter.

The approach improves the reliability of sinusoidal/exponential signal modeling.

Abstract

The Prony method for approximating signals comprising sinusoidal/exponential components is known through the pioneering work of Prony in his seminal dissertation in the year 1795. However, the Prony method saw the light of real world application only upon the advent of the computational era, which made feasible the extensive numerical intricacies and labor which the method demands inherently. The Adaptive LMS Filter which has been the most pervasive method for signal filtration and approximation since its inception in 1965 does not provide a consistently assured level of highly precise results as the extended experiment in this work proves. As a remedy this study improvises upon the Prony method by observing that a better (more precise) computational approximation can be obtained under the premise that adjustment can be made for computational error , in the autoregressive model setup in the initial step of the Prony computation itself. This adjustment is in proportion to the deviation of the coefficients in the same autoregressive model. The results obtained by this improvisation live up to the expectations of obtaining consistency and higher value in the precision of the output (recovered signal) approximations as shown in this current work and as compared with the results obtained using the Adaptive LMS Filter.