Empirical mode decomposition: an analytical approach for sifting process

The present letter proposes an alternate procedure that can be effectively employed to replace the essentially algorithmic sifting process in Huang's empirical mode decomposition (EMD) method. Recent works have demonstrated that EMD acts essentially as a dyadic filter bank that can be compared to wavelet decompositions. However, the origin of EMD is algorithmic in nature and, hence, lacks a solid theoretical framework. The present letter proposes to resolve the major problem in the EMD method-the mean envelope detection of a signal-by a parabolic partial differential equation (PDE)-based approach. The proposed approach is validated by employing several numerical studies where the PDE-based sifting process is applied to some synthetic composite signals.