**DAUBECHIES' WAVELETS**
were discovered at the end of the eighties
after Meyer's and S.Mallat's works on multiresolution analysis. Inspired by the famous
work of Alex Grossman and Jean Morlet on fluctuation detection in seismic signals,
these authors opened an outstanding chapter on applied mathematics, bringing together
in one stroke a large number of domains to study a single question : how to characterise
what is local (in space), short lived (in time) or similar on all scales? This
question touches many fields such as quantum mechanics (coherent states and Klauder's
works), signal processing (image coding and pyramidal algorithms by Burt and Adelson),
approximation theory (interpolation schemes by Dubuc and Deslauriers) and harmonic
analysis (Holderian regularity of functions). It was answered by the manufacture
of a "mathematical microscope" built from special functions called wavelets which
may be used to extract the details of a function,a signal or a measure. A famous
result of Low and Balian on time-frequency representations suggested the
impossibility of creating an "ideal microscope" with space accuracy,
good frequency resolution and stable signal representation. Nevertheless,
Ingrid Daubechies showed that these properties were available which came to be
known as the Daubechies's wavelets...