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   -> Volume 6, Issue 11

Book: Wavelets and Turbulence (in French)
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Patrice Abry (

PostPosted: Wed Oct 29, 1997 9:26 am    
Subject: Book: Wavelets and Turbulence (in French)
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#2 Book: Wavelets and Turbulence (in French)

This is to ammounce the publication of a new book in French on
Wavelets and Turbulence.

Ondelettes et Turbulence - Multiresolutions, algorithmes de
decompositions, invariance d'echelle et signaux de pression.

Patrice ABRY

Preface de Patrick Flandrin.

Octobre 1997. 289 pages. ISBN - 2-84134-064-3

DIDEROT DMF, 22, rue Malher, 75004 Paris France.
Tel: (33) (0)1 44 54 03 15
Fax: (33) (0)1 44 54 03 16


The first chapter consists in a thorough presentation of the wavelet
analysis. Systematic comparisons of the definitions and properties of
the various, continuous or discrete, redundant and non redundant,
orthogonal, semi- or bi-orthogonal, transforms enable us to propose
some pieces of answer to the questions one should ask before using
this tool to analyse experimental data: is time-scale analysis the
relevant description, which form of the transform should be used,
which wavelet and which algorithm should be chosen? In the second
chapter, we allow a larger part to the multiresolution analysis and to
the possibility of designing an infinite variety of (semi-, bi-)
orthogonal wavelets, which correspond to a priori chosen analysing
patterns. Chapter three proposes a study of the scale invariance
phenomenon through three different applications for which the
relevance of wavelet decomposition coefficients as a space of
representation is widely discussed and underlined: spectral estimation
devoted to $1/f$ and self-similar processes, fractal and long-range
dependance analysis in point processes, wide-band transient
detection. We finally present, in the last chapter, results obtained,
thanks to time-scale analyses, from pressure signals originating from
a developed turbulence experiment. We describe, in particular, some
features of the vorticity filaments, which are coherent structures in
turbulent flows. We also study the intermittency phenomenon by
cancelling, in signals, pressure drops. To do so, we manipulate the
wavelet coefficients which coincide with the arrivals of these
pressure drops.
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