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   -> Volume 3, Issue 2


Preprints available
 
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Author Message
Akram Aldroubi, aldroubi@helix.nih.gov
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PostPosted: Mon Dec 02, 2002 11:32 am    
Subject: Preprints available
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Preprints available

Reprint available: "Familes of multiresolution and wavelet spaces with
optimal properties"
by Akram Aldroubi and Michael Unser, in Numer. Funct. Anal. an Optimiz.,
pp. 417-446, 1993.

Also available, preprint of the paper below. To receive copies, please send
your postal address by email to: aldroubi@helix.nih.gov

Designing MRA-type wavelets and their fast algorithms

By
Patrice Abry, Ecole Normale Superieure de Lyon, France
and
Akram Aldroubi, National Institutes of Health, USA

Often, the Discrete Wavelet Transform is performed and
implemented with the Daubechies wavelets, the Battle-Lemarie wavelets or
the splines wavelets whereas in continuous time wavelet decomposition a much
larger variety of mother wavelets are used. Maintaining the dyadic
time-frequency
sampling and the recursive pyramidal computational structure, we present
various
methods to obtain any chosen analyzing wavelet $psi_{wanted}$, with some
desired
shape and properties and which is associated with a semi-orthogonal
multiresolution
analysis. We explain in details how to design one's own wavelet, starting from
any given Multiresolution Analysis. We also explicitly derive the formulae
of the
filter bank structure that implements the designed wavelet. We illustrate these
wavelet design techniques with examples that we have programmed with Matlab
routines.
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