  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/.
