Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency analysis

TL;DR

This paper introduces the Adaptive Local Iterative Filtering (ALIF) method, an innovative, stable, and local signal decomposition technique that improves time-frequency analysis of non-linear, non-stationary signals using data-driven filters.

Contribution

It proposes the ALIF method with adaptive filter length selection and introduces FP-based smooth filters, ensuring convergence and enhanced stability for signal decomposition.

Findings

ALIF achieves effective signal decomposition with improved stability.

FP filters satisfy convergence conditions for iterative filtering.

Numerical examples demonstrate superior performance of ALIF and IF methods.

Abstract

Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time-frequency analysis can be applied more effectively. In this paper we consider the iterative filters (IFs) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IFs applied to any $L^2$ signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IFs strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker-Planck equations (FP filters) that can be used within both IFs and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IFs algorithm. Numerical examples are given to demonstrate the performance and stability of IFs and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose a new definition for the instantaneous frequency which depends exclusively on local properties of a signal.