. 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 essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.Index Terms-Empirical Mode Decomposition, filter banks, wavelets, fractional Gaussian noise. I. EMD BASICST HE starting point of the Empirical Mode Decomposition (EMD) is to consider signals at the level of their local oscillations. Looking at the evolution of a signal x(t) between two consecutive local extrema (say, two minima occurring at times t − and t + ), we can heuristically define a (local) highfrequency part {d(t),corresponds to the oscillation terminating at the two minima and passing through the maximum which necessarily exists in between them. For the picture to be complete, we also identify the corresponding (local) low-frequency part m(t), or local trend, so that we have x(t) = m(t) + d(t) for t − ≤ t ≤ t + . Assuming that this is done in some proper way for all the oscillations composing 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, considered as a new signal to decompose, and successive constitutive components of a signal can therefore be iteratively extracted, 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 x(t), the effective algorithm of EMD can be summarized as follows [2]: 1) identify all extrema of x(t) 2) interpolate between minima (resp. maxima), ending up with some "envelope" e min (t) (resp. e max (t)) 3) compute the average m(t) = (e min (t) + e max (t))/2 4) extract the detail d(t) = x(t) − m(t) 5) iterate on the residual m(t) In practice, the above procedure has to be refined by a sifting process which amounts to first iterating steps 1 to

The purpose of this paper is to evidence why wavelet-based estimators are naturally matched to the spectrum analysis of 1/ f processes. It is shown how the revisiting of classical spectral estimators from a time-frequency perspective allows to define different wavelet-based generalizations which are proved to be statistically and computationally efficient. Discretization issues (in time and scale) are discussed in some detail, theoretical claims are supported by numerical experiments and the importance of the proposed approach in turbulence studies is underlined.1 On 1/ f processes 1.1 Power-law spectra and self-similarity Signals with power-law spectra -or "1/1 processes," i.e., stochastic signals X(t) such that their power spectrum density rx(v) is proportional to Ivl-o over some decadesare ubiquitous in fields such as physics, biology, engineering or economics, to name but a few [K2]. In turbulence for instance [81]' the spectrum of the velocity field is known to obey a power-law decay over a wide range of frequencies (the so-called inertial range) with an exponent 0: ~ 5/3. In this case, a very accurate measurement of the spectral exponent is highly desirable, since its value is of a key importance for discriminating between competing theories. Generally speaking, 1/1 behaviors at low frequencies are associated with slowly-decaying correlations, and the interest for 1/1 processes has also been recently renewed by the development of chaos phenomenology, according to which an apparently stochastic behavior can in fact result from a deterministic mechanism with long-range dependent characteristics [MC].From another perspective, power-law spectra indicate that a signal exists at all scales

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.