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.