Derivative-optimized Empirical Mode Decomposition for the Hilbert-Huang Transform

In the Empirical Mode Decomposition EMD for the Hilbert-Huang Transform HHT a nonlinear and nonstationary signal is adaptively decomposed by 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 upper envelope consisting of local maxima and lower envelopes 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 HHT. To reduce such uncertainty, the 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.