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Empirical mode decomposition

The process of EMD has the following simple expression:

$\displaystyle s(t)=\sum_{n=1}^{N}c_n(t)+r(t),$ (1)

where $ s(t)$ is the original non-stationary signal, $ c_n(t)$ ( $ n=1,2,\cdots,N$ ) denotes each separated IMF, $ N$ denotes the number of separated IMF, and $ r(t)$ denotes the residual after EMD. The process of EMD is to gradually remove the stable oscillations embedded in the original signal to arrive at a monotonic and smooth residual or trend at last. A special property of the EMD is that the IMFs represent different oscillations embedded in the data, where the oscillating frequency for each sub-signal $ c_n(t)$ decreases with IMF order increasing (Huang et al., 1998).