Compute the multifractal spectrum by the wavelet leaders

Ideas
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1

Hello,

I work in multifractal analysis of processes and I make my spectrum simulations or p-exponents calculations with Matlab. Indeed, H. Wendt developed a toolbox on Matlab to make these simulations (Herwig Wendt).
But I have several problems:

  • I don’t like Matlab
  • Mathematica has developed many tools for wavelet analysis: CWT, DWT, etc.
  • I like Mathematica.

I would like to create two codes to determine the multifractal spectrum in two different ways:

  1. Compute the spectrum with Wavelet Leaders.
  2. Compute the spectrum with WTMM (Wavelet transform modulus maxima).
    In the thesis of H. Wendt (https://www.irit.fr/~Herwig.Wendt/data/ThesisWendt.pdf), these methods are explained in detail.

The aim for the moment is to create a code with Wavelet Leader and to run this code for sample processes: fBm (fractional Brownian motion), economic or images…
I would like to have the experience of this community: Does such code exist? Are there any books? Your advice and remarks :).

Thanks!

Best regards,

Guillaume Saës

PS : Sorry for my English ^^

2

I have write two programs for multifractal analysis of series, one with DFA method and another with Wavelet method, but not with WTMM or with Wavelet Leaders.
André Dauphiné

MultiFractalSerieDFABon.nb (65.8 KB)
MultiFractalSerieOndelettesBon.nb (67.9 KB)

1 Like
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I hesitated to contact you
Thank you very much ^^

4

HELLO,
Please i need the Wavelets Package for Mathemetica 5.0
Who can help me?