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

We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decom-position (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 param-eters 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 su-periority over the other existing 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