Nonlinear Mode Decomposition: a new noise-robust, adaptive decomposition method

TL;DR

Nonlinear Mode Decomposition (NMD) is a noise-robust, adaptive method that decomposes signals into meaningful oscillations, outperforming existing techniques and applicable across various scientific fields.

Contribution

The paper introduces NMD, a novel adaptive decomposition method combining time-frequency analysis and surrogate data tests, offering superior noise robustness and applicability.

Findings

NMD effectively decomposes signals into meaningful oscillations.

NMD outperforms existing methods like EMD and ICA.

NMD is applicable to diverse real-world signals.

Abstract

We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques - which together with the adaptive choice of their parameters make it extremely noise-robust - and surrogate data tests, used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals, and demonstrate its qualitative and quantitative superiority over the other existing approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loeve expansion and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary MATLAB codes for running NMD are freely available at http://www.physics.lancs.ac.uk/research/nbmphysics/diats/nmd/.