Brief review of EMD

EMD is an adaptive signal analysis algorithm that decomposes a non-stationary 1D signal into multiple stationary sub-signals:

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

where $s(t)$ is a non-stationary 1D signal and $c_n(t)$ is $n$th decomposed stationary signal, which is also called intrinsic mode function (IMF). $r(t)$ is the monotonic residual. $N$ is the number of IMFs.

The decomposition is achieved via a recursive process called sifting algorithm. There are four main steps in the sifting algorithm: firstly, finding the local maxima and minima of the signal, and then fitting those extrema by cubic spline interpolation in order to obtain the upper and lower envelopes; secondly, calculating the mean of upper and lower envelopes and subtracting it from the original signal; thirdly, recursively implementing the first two steps until the remaining signal satisfy the two criteria of IMF: (1) the number of extrema and the number of zero crossing points cannot differ by more than one; (2) the mean value of upper envelope and lower envelope must be zero Huang et al. (1998); fourthly, subtracting the obtained IMF from the original signal and implementing the aforementioned three steps recursively on the remaining signal until the residual $r(t)$ becomes either too small or a monotonic function.