Instantaneous Frequency Estimation in Noisy Multicomponent Signals with Interfering Modes Based on Prony Method and Spline Approximation

TL;DR

This paper introduces a new method combining Prony's approach with spline approximation to accurately estimate instantaneous frequencies in noisy, multicomponent signals with closely spaced modes, overcoming interference issues.

Contribution

It presents a novel algorithm that effectively reduces oscillations in IF estimates caused by mode interference using spline approximation, enhancing estimation accuracy in challenging noisy conditions.

Findings

Improved IF estimation accuracy in noisy multicomponent signals.

Effective removal of oscillations caused by mode interference.

Demonstrated benefits through numerical simulations.

Abstract

In this paper, we propose a novel estimator of the instantaneous frequencies (IFs) of the modes making up multicomponent signals (MCSs). We are particularly interested in dealing with noisy MCSs containing close modes in the time-frequency plane. Though it is possible to adapt Prony approach to estimate IFs in such situations, interference between the modes generates oscillations in the obtained estimations. After having investigated the nature of these oscillations, we propose an algorithm to remove these in IFs estimation, based on spline approximation. Numerical applications in various situations illustrate the benefit of mixing Prony technique with spline approximation for IF estimation in noisy MCSs containing close modes.