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.