Empirical Mode Decompositions as Data-Driven Wavelet-like Expansions

Huang's data-driven technique of Empirical Mode Decomposition (EMD) is applied to the versatile, broadband, model of fractional Gaussian noise (fGn). The experimental spectral analysis and statistical characterization of the obtained modes reveal an equivalent filter bank structure which shares most properties of a wavelet decomposition in the same context, in terms of self-similarity, quasi-decorrelation and variance progression. Furthermore, the spontaneous adaptation of EMD to "natural" dyadic scales is shown, rationalizing the method as an alternative way for estimating the fGn Hurst exponent.

[1]  K. Coughlin,et al.  11-Year solar cycle in the stratosphere extracted by the empirical mode decomposition method , 2004 .

[2]  Régis Fournier.  Analyse stochastique modale du signal stabilométrique : application à l'étude de l'équilibre chez l'homme , 2002 .

[3]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[4]  Gabriel Rilling,et al.  Empirical mode decomposition as a filter bank , 2004, IEEE Signal Processing Letters.

[5]  Gabriel Rilling,et al.  On empirical mode decomposition and its algorithms , 2003 .

[6]  Patrice Abry,et al.  Wavelets for the Analysis, Estimation, and Synthesis of Scaling Data , 2002 .

[7]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[8]  Patrick Flandrin,et al.  Time-Frequency/Time-Scale Analysis , 1998 .

[9]  N. Huang,et al.  A study of the characteristics of white noise using the empirical mode decomposition method , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[10]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  E P Souza Neto,et al.  Assessment of Cardiovascular Autonomic Control by the Empirical Mode Decomposition , 2004, Methods of Information in Medicine.

[12]  B. Anderson,et al.  Simulation of stationary stochastic processes , 1968 .

[13]  A. Wood,et al.  Simulation of Stationary Gaussian Processes in [0, 1] d , 1994 .