An adaptive data analysis method for nonlinear and nonstationary time series: The empirical mode decomposition and Hilbert Spectral Analysis

An adaptive data analysis method, the Empirical Mode Decomposition and Hilbert Spectral Analysis, is introduced and reviewed briefly. The salient properties of the method is emphasized in this review; namely, physical meaningful adaptive basis, instantaneous frequency, and using intra-wave frequency modulation to represent nonlinear waveform distortion. This method can perform and enhance most of the traditional data analysis task such as filtering, regression, and spectral analysis adaptively. Also presented are the mathematical problems associated with the new method. It is hope that this presentation will entice the interest of the mathematical community to examine this empirically based method and inject mathematical rigor into the new approach.