Empirical Mode Decomposition as a Filter Bank

Abstract

Abstract—Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonsta-tionary signals as sums of zero-mean amplitude modulation fre-quency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essen-tially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the ex-tracted modes may be similarly exploited for getting access to the Hurst exponent. Index Terms—Empirical mode decomposition (EMD), filter banks, fractional gaussian noise, wavelets. I. EMD BASICS THE STARTING point of the empirical mode decomposi-tion (EMD) is to consider signals at the level of their local oscillations. Looking at the evolution of a signal between two consecutive local extrema (say, two minima occurring at times and), we can heuristically define a (local) high-fre-quency part. Also called detail, cor-responds to the oscillation terminating at the two minima and passing through the maximum which necessarily exists in be-tween them. For the picture to be complete, we also identify the corresponding (local) low-frequency part, or local trend, so that we have for. Assuming that this is done in some proper way for all the oscillations com-posing the entire signal, we get what is referred to as an intrinsic mode function (IMF) as well as a residual consisting of all local trends. The procedure can then be applied to this residual, con-sidered as a new signal to decompose, and successive consti-tutive components of a signal can therefore be iteratively ex-tracted, the only definition of such a so-extracted “component” being that it is locally (i.e., at the scale of one single oscillation) in the highest frequency band. Given a signal, the effective algorithm of EMD can be summarized as follows [2]. 1) Identify all extrema of. 2) Interpolate between minima (resp. maxima), ending up with some “envelope ” (resp.). 3) Compute the average. 4) Extract the detail. 5) Iterate on the residual.

Keywords

Affiliated Institutions

• Centre National de la Recherche Scientifique FR
• École Normale Supérieure de Lyon FR
• Laboratoire de l'Informatique du Parallélisme FR

Related Publications