Methods of Analysis

Lesson

Introduction
Trace Moments (TM)
Double Trace Moments (DTM)
Probability Distribution Multiple Scaling
Structure Function
Empirical Modal Decomposition (EMD)
- Introduction
- Method Principle
- Algorithm
- Applications: geophysics flows
Exercises
Conclusion

Algorithm

Norden Huang et al (1998) introduced the EMD algorithm called by himself "sifting process", to decompose some signal into several IMFs. The corresponding algorithm corresponds to the following steps :

The identification of the local extrema : this step is provided by the zeros values of the signal derivative.

Connection of the local maxima (resp. minima) in order to obtain the upper envelop (resp. lower envelop ): the connection is provide by spline cubic interpolation.

Average estimation:

Subtraction of the mean in order to obtain the IMF:

The right animation shows the principle of subtraction of the first IMF.

Sketch of sifting process for EMD algorithm

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