Abstract
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, 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 other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève 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 for download.
Highlights
Complex systems in real life are commonly studied by analysis of the signals that they generate
We develop a set of criteria in which almost all nonlinear mode decomposition (NMD) settings can be adapted automatically to the signal, greatly improving its performance and making it a kind of superadaptive approach
This statistics is directly related to the quality of the representation of component in the signal’s time-frequency representation (TFR), so that the significance of the surrogate test based on it reflects the proportion of the “deterministic” part in the extracted amplitude and frequency dynamics
Summary
Complex systems in real life are commonly studied by analysis of the signals that they generate. Both of these methods are generally susceptible to the time shifts and the number of blocks used to create the multivariate signal from the original one (as was demonstrated, e.g., in [11] for the Karhunen-Loeve expansion), suffering from the drawback (1) Another approach, which is becoming increasingly popular, is to use a particular time-frequency representation (TFR) [12,13,14,15,16,17] of the signal, e.g., the wavelet transform, for decomposing it into separate modes. The flaws mentioned greatly restrict the applicability of the approaches currently in use, so that only for a very small class of signals can the decomposition be carried out successfully To overcome these limitations, we introduce nonlinear [26] mode decomposition (NMD). IX and the full NMD procedure is summarized in the Appendix
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