A Spectral Approach for Sifting Process in Empirical Mode Decomposition

Abstract

In this paper, we propose an alternative to the algorithmic definition of the sifting process used in the original Huang's empirical mode decomposition (EMD) method. Although it has been proven to be particularly effective in many applications, EMD method has several drawbacks. The major problem with EMD is the lack of theoretical Framework which leads to difficulties for the characterization and evaluation this approach. On top of the mathematical model, there are other concerns with mode mixing and transient phenomena, such as intermittency or pure tones separation. This paper follows a previous published nonlinear diffusion-based filtering to solve the mean-envelope estimation in sifting process. The major improvements made in this present work are a non-iterative resolution scheme for the previously proposed partial differential equation (PDE), a new definition of the stopping function used in the PDE framework, and finally an automatic regularization process based on inverse problem theory to deal with mode mixing or transient detection problem. Obtained results confirm good properties of the new version of the PDE-based sifting process and its usefulness for decomposition of various kinds of data. The efficiency of the method is illustrated on some examples using informative and pathological signals for which standard EMD algorithm fails.