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Paulo Gonçalves Inria senior researcher in the project DANTE A joint team of Inria Rhone-Alpes and ENS Lyon (LIP) |
| Signal Processing applied to Networks | ||
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Time-Frequency Analysis Time-Scale Analysis |
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Wavelets and Fractals Wavelets History by I. Daubechies |
Description: Fractional Brownian motion (fBm) has for long served as the archetype
of a process with long range dependence (LRD). At the same time,
positive increment processes such as multiplicative cascades have
proven amenable models for processes with underlying multifractal
structures. For both processes, wavelets have played a key role in
their analysis and synthesis. Combining these two classes of processes
in the so-called fractional Brownian motions in multifractal
time (BM(MT)) a novel class of processes was introduced by B. Mandelbrot,
which are versatile enough to enable modeling of LRD and multifractal
scaling independently. In our pioneering study, we proposed an exact wavelet-based synthesis of these compound multifractal processes. Rationale is first to decompose a realization of H-fbm into a wavelet basis (imposing so the wavelet tree statistic structure). The wavelet coefficients are then weighted by the multifractal measure subordinators to feed the model with multifractal time. The (BM(MT)) is then obtained by inverting the so-modified wavelet decomposition. Joint work with: Rudolf Riedi |
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| Wavelets and Statistics | ||
| Other applications |
