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m clean up punctuation and spacing issues, primarily spacing around commas, replaced: ,C → , C, ,D → , D, ,i → , i (40), ,j → , j (44), ,k → , k (2), ,l → , l, ,n → , n (10), ,q → , q (3), ,t → , t (15), ,x → , x (4), ,y → , y (4 |
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==Ensemble empirical mode decomposition==
To improve the accuracy of measurements, the ensemble mean is a powerful approach, where data are collected by separate observations, each of which contains different noise over an ensemble of universe's. 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 i th ‘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 not arbitrary but different copies of white noise, wi(t), to that single observation as given in the equation. Although adding noise may result in 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 does not affect the decomposition
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