Smoothing empirical mode decomposition: A patch to improve the decomposed accuracy

Hilbert-Huang Transformation (HHT) is designed especially for analyzing data from nonlinear and nonstationary processes. It consists of the Empirical Mode Decomposition (EMD) to generate Intrinsic Mode Function (IMF) components, from which the instantaneous frequency can be computed for the time-frequency Hilbert spectral Analysis. Currently, EMD, based on the cubic spline, is the most efficient and popular algorithm to implement HHT. However, EMD as implemented now suffers from dependence on the cubic spline function chosen as the basis. Furthermore, due to the various stoppage criteria, it is difficult to establish the uniqueness of the decomposition. Consequently, the interpretation of the EMD result is subject to certain degree of ambiguity. As the IMF components from the classic EMD are all approximations from the combinations of piece-wise cubic spline functions, there could also be artificial frequency modulation in addition to amplitude modulation. A novel Smoothing Empirical Mode Decomposition (SEMD) is proposed. Although SEMD is also an approximation, extensive tests on nonlinear and nonstationary data indicate that the smoothing procedure is a robust and accurate approach to eliminate the dependence of chosen spline functional forms. Thus, we have proved the uniqueness of the decomposition under the weak limitation of spline fittings. The natural signal length-of-day 19651985 was tested for the performance in nonstationary and nonlinear decomposition. The resulting spectrum by SEMD is quite stable and quantitatively similar to the optimization of EMD.