Paulo Gonçalves

Inria senior researcher in the project DANTE
A joint team of Inria Rhone-Alpes and ENS Lyon (LIP)

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Signal Processing applied to Networks
Time-Frequency Analysis
Time-Scale Analysis
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
Wavelets and Statistics
Other applications

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