Abstract：Traditionally, we process data under the linear and stationary assumptions.  The existing methods on probability theory and spectral analysis are all based on the stationary and linear assumptions.  For example, spectral analysis is synonymous with the Fourier based analysis.  As Fourier spectrum can only give meaningful interpretation to linear and stationary process, its application to data from nonlinear and nonstationary processes is problematical.  To break away from these limitations, we should let data speak for themselves.  We should develop adaptive data analysis techniques, for the world we live in is neither stationary nor linear. 

A new method, the Empirical Mode Decomposition (EMD) method, for analyzing, not simply processing, nonlinear and nonstationary data has been proposed.  The key part EMD is to decompose any complicated data set into a finite and often small number of Intrinsic Mode Functions (IMF).  An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively.  This decomposition method is adaptive, highly efficient and usually retains full physical meaning of the underlying driving mechanisms.  The IMF serves as a posteriori basis for the data.  As such, EMD gives an extremely sparse representation of the data with both amplitude and frequency modulated; it is much more general than any expansion based on a priori basis.  IMF also admits well-behaved Hilbert transform. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time  that give sharp identifications of imbedded structures of the data. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum.  Since the decomposition is based on the local characteristic time scale of the data, it is applicable to data from nonlinear and nonstationary processes.  Classical nonlinear system models are used to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution. 

At this stage, the method is still empirically based.  Though it is powerful in solving practical problems, to make it mathematically rigorous we still face many challenging problems both theoretical and practical.  Further developments are urgently needed.