Empirical mode decomposition (EMD) is a data-driven decomposition method and was originally proposed by Huang et. al in 1998 [1]. Since that time the method has gained a lot of attention in the science community. EMD has been applied in a wide range of different fields, including geophysics, biomedicine, neuroscience, finance and many more.

The method is defined by an algorithm as follows:

- Identify all local extrema (both minima and maxima) in input signal .
- If the number of extrema is less or equal 2 then is considered as a trend ( ) — finish with one component.
- Estimate top (env_max) and bottom(env_min) envelopes by interpolating respectively local maxima and local minima with natural cubic splines.
- Calculate local mean (mean of both envelopes) — .
- Subtract the mean from the input signal .
- If fulfills the stopping criteria, then it is considered an intrinsic mode function (IMF) (a component ) and algorithm starts again from step 1 for a signal . Otherwise, it starts with .

Empirical evidence is that the algorithm converges to finite number of IMFs, with which input signal can be reconstructed :

where is the number of components.

[1] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, *“The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,”* Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 454, pp. 903-995, 1998.