where is a non-stationary 1D signal and is th decomposed stationary signal, which is also called intrinsic mode function (IMF). is the monotonic residual. 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 becomes either too small or a monotonic function.

2020-02-21