# On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition

Another of my papers [1] (see About) has been published recently. Unfortunately, I cannot present it here in a full scope. Below I'm presenting an abstract from the paper and invite interested people in contacting me. This topic is really interesting and there is plenty to be done.

**On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition**

Abstract:
*This paper investigates frequency mixing effect of Empirical Mode Decomposition (EMD) and explores whether it can be explained by simple phase coupling between components of the input signal. The input is assumed to be a linear combination of harmonic oscillators. The hypothesis was tested assuming that phases of input signals' components would couple according to Kuramoto's model. Using a Kuramoto's model with as many oscillators as the number of intrinsic mode functions (result of EMD), the model's parameters were adjusted by a particle swarm optimisation (PSO) method. The results show that our hypothesis is plausible, however, a different coupling mechanism than the simple sine-coupling Kuramoto's model are likely to give better results.*

In a very, very brief, but figure-enhanced summary: we present that for certain range of frequencies ratio a mix in frequency appears which can be explained as a difference of original frequencies. Figure below presents Fourier transform *F* of correlation function between each pair of IMFs for different values of frequency f. All values were normalised, such that for given f the maximum is equal to one. Additionally, on the top projection of the figure two lines have been drawn - F1 = 13-f (dashed line) and F2 = 2(13 - f) (dash-dotted line).

[1] D. Laszuk, O. J. Cadenas, and S. J. Nasuto (July, 2016) **On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition**, Advances in Data Science and Adaptive Analysis, vol. 8, no. 1. [Link]