Random noise attenuation by - empirical mode decomposition predictive filtering |

In this appendix, we review the sifting algorithm of empirical mode decomposition (equation 6 in the main paper). For the original signal, we first find the local maxima and minima of the signal. Once identified, fit these local maxima and minima by cubic spline interpolation in turn in order to generate the upper and lower envelopes. Then compute the mean of the upper and lower envelopes , the difference between the data and first mean .

where denotes the remaining signal after th sifting for generating the th IMF, and are corresponding upper and lower envelopes, respectively, and is the mean of upper and lower envelopes after th sifting for generating the th IMF. Repeating the sifting procedure (A-2) times, until reach the prerequisites of IMF, these are:

The criterion for the sifting process to stop is given by Huang et al. (1998) as:

where denotes the standard deviation. When is considered as an IMF, let , we separate the first IMF from the original data:

where is the original signal, denotes the th IMF, and is the residual after the th IMF based sifting. Repeating the sifting process from equation A-1 to A-5, changing to , in order to get the following IMFs: . The sifting process can be stopped when the residual , becomes so small that it is less than a predetermined value of substantial consequence, or when becomes a monotonic function from which no more IMF can be extracted.

Finally, we achieved a decomposition of the original data into N modes, and one residual, as shown in equation 6 in the main context.

Random noise attenuation by - empirical mode decomposition predictive filtering |

2014-08-20