Derivative-optimized empirical mode decomposition for the Hilbert-Huang transform
Abstract
In the empirical mode decomposition (EMD) for the Hilbert–Huang transform (HHT), a
nonlinear and non-stationary signal is adaptively decomposed by an HHT into a series
of intrinsic mode functions (IMFs) with the lowest one as the trend. At each step of the
EMD, the low-frequency component is mainly determined by the average of the upper
envelope (consisting of local maxima) and the lower envelope (consisting of local minima).
The high-frequency component is the deviation of the signal relative to the low-frequency
component. The fact that no local maximum and minimum can be determined at the two
end-points leads to detrend uncertainty, and in turn causes uncertainty in the HHT. To
reduce such uncertainty, Hermitian polynomials are used to obtain the upper and lower
envelopes with the first derivatives at the two end-points (qL
, qR) as parameters, which are
optimally determined on the base of minimum temporal variability of the low-frequency
component in the each step of the decomposition. This well-posed mathematical system is
called the Derivative-optimized EMD (DEMD). With the DEMD, the end effect, and detrend
uncertainty are drastically reduced, and scales are separated naturally without any a priori
subjective selection criterion.
Description
Journal of Computational and Applied Mathematics, in press
The article of record as published may be located at http://dx.doi.org/10.1016/j.cam.2013.03.046
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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