A Reinterpretation of EMD by cubic spline interpolation

Empirical mode decomposition (EMD) is a data-driven technique that decomposes a signal into several zero-mean oscillatory waveforms according to the levels of oscillation. Most of the studies on EMD have focused on its use as an empirical tool. Recently, Rilling and Flandrin [2008] studied theoretical aspects of EMD with extensive simulations, which allow a better understanding of the method. However, their theoretical results have been obtained by considering constraints on the signal such as equally spaced extrema and constant frequency. The present study investigates the theoretical properties of EMD using cubic spline interpolation under more general conditions on the signal. This study also theoretically supports modified EMD procedures in Kopsinis and Mclaughlin [2008] and developed for improving the conventional EMD. Furthermore, all analyses are preformed in the time domain where EMD actually operates; therefore, the principle of EMD can be visually and directly captured, which is useful in interpreting EMD as a detection procedure of hidden components.