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Article Dans Une Revue Physical Review E Année : 1993

Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method

Résumé

Several attempts have been made recently to generalize the multifractal formalism, originally introduced for singular measures, to fractal signals. We report on a systematic comparison between the structure-function approach, pioneered by Parisi and Frisch [in 2 Proceedings of the International School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by M. Ghil, R. Benzi, and G. Parisi (North-Holland, Amsterdam, 1985), p. 84] to account for the multifractal nature of fully developed turbulent signals, and an alternative method we have developed within the framework of the wavelet-transform analysis. We comment on the intrinsic limitations of the structure-function approach; this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases. We demonstrate that our method, based on the wavelet-transform modulus-maxima representation, works in most situations and is likely to be the ground of a unified multifractal description of self-affine distributions. Our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations.
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hal-01557138 , version 1 (05-07-2017)

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Jean-François Muzy, Emmanuel Bacry, Alain Arnéodo. Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. Physical Review E , 1993, 47 (2), pp.875-884. ⟨10.1103/PhysRevE.47.875⟩. ⟨hal-01557138⟩
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