
Paulo Gonçalves Inria senior researcher in the project DANTE A joint team of Inria RhoneAlpes and ENS Lyon (LIP) 
Signal Processing applied to Networks  
TimeFrequency Analysis TimeScale Analysis 

Wavelets and Fractals Wavelets History by I. Daubechies 
Description: Processes with continuous but highly irregular paths occur quite
commonly in a host of applications. For cascading measures, e.g, such discontinuities convey
most of the pertinent information and their relevance is widely agreed upon. More generally, various
complex systems are known to produce signals in which singularities may coexist in great multitude
and in a highly interwoven interplay. The local degree of Holder regularity H(t) becomes
then so utterly erratic as a function of location $t that its pointwise estimation becomes
completely unrealistic. With the estimation of H(t) point by point infeasible one resorts to the "multifractal formalism" which allows to quantify how frequently a given singularity strength H(t)=h is assumed, where frequency can be measured in geometrical or probabilistic terms (as the location t is chosen randomly). Consequently, several notions of socalled multifractal spectra have been proposed to quantify this occurrence in various terms. In different directions, our work focused on:


Wavelets and Statistics  
Other applications 