Multidimensional empirical mode decomposition: Difference between revisions

Revision as of 04:07, 4 July 2022

Revision as of 06:48, 15 July 2022

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==Ensemble empirical mode decomposition==

The ensemble mean is an approach to improveimproving the accuracy of measurements. Data are collected by separate observations, each of which contains different noise over an ensemble of universes. To generalize this ensemble idea, noise is introduced to the single data set, <math>x(t)</math>, as if separate observations were indeed being made as an analogue to a physical experiment that could be repeated many times. The added [[white noise]] is treated as the possible random noise that would be encountered in the measurement process. Under such conditions, the ‘artificial’ observation will be <math>x_i(t)=x(t)+w_i(t)</math>.

In the case of only one observation, one of the multiple-observation ensembles is mimicked by adding different copies of white noise, <math>w_i(t)</math>, to that single observation as given in the equation. Although adding noise may result in a smaller signal-to-noise ratio, the added white noise will provide a uniform reference scale distribution to facilitate EMD; therefore, the low signal-noise ratio will not affect the decomposition method but actually enhances it by avoiding mode mixing. Based on this argument, an additional step is taken by arguing that adding white noise may help extract the true signals in the data, a method that is termed Ensemble Empirical Mode Decomposition (EEMD).

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In these steps, EEMD uses two properties of white noise:

# The added white noise leads to a relatively even distribution of extrema distribution on all timescales.

# The [[Dyadic transformation|dyadic]] filter bank property provides a control on the periods of oscillations contained in an oscillatory component, significantly reducing the chance of scale mixing in a component. Through ensemble average, the added noise is averaged out.<ref name=":9" />