The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis
Abstract
A new method for analysing nonlinear and nonstationary data has been developed. The key part of the method is the 'empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit wellbehaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energyfrequencytime distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of 'intrinsic mode functions' based on local properties of the signal, which make the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and nonstationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. Classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and nonstationary effects in the energyfrequencytime distribution.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 March 1998
 DOI:
 10.1098/rspa.1998.0193
 Bibcode:
 1998RSPSA.454..903H