One or two frequencies? The Iterative Filtering answers

TL;DR

This paper investigates the capability of the Iterative Filtering method to distinguish between one or two close frequencies in non-stationary signals, providing new theoretical insights and numerical evidence.

Contribution

It offers new theoretical results and numerical analysis on the effectiveness of Iterative Filtering in separating two close frequencies, addressing a key open problem.

Findings

Iterative Filtering can effectively separate two close frequencies under certain conditions.

Theoretical analysis supports the numerical evidence of frequency separation capabilities.

The method's ability to distinguish frequencies depends on specific signal properties.

Abstract

The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode Decomposition, has been used extensively in many applied fields of research and studied, from a mathematical point of view, in several papers published in the last few years. However, even if its convergence and stability are now established both in the continuous and discrete setting, it is still an open problem to understand up to what extent this approach can separate two close-by frequencies contained in a signal. In this paper, following the studies conducted on the Empirical Mode Decomposition and the Synchrosqueezing methods, we analyze in detail the abilities of the Iterative Filtering algorithm in extracting two stationary frequencies from a given signal. In particular, after reviewing the Iterative Filtering technique and its known properties, we present new theoretical results and numerical evidence showing the ability of this technique in addressing the fundamental "one or two frequencies" question.