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   -> Volume 2, Issue 18


Preprint available: Complex Daubechies wavelets
 
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lina@lps.umontreal.ca (Jean-Marc Lina)
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PostPosted: Fri Nov 29, 2002 3:40 pm    
Subject: Preprint available: Complex Daubechies wavelets
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Preprint available: Complex Daubechies wavelets

Preprint available: Request pre-print by e-mail to lina@lps.umontreal.ca

COMPLEX DAUBECHIES WAVELETS

Jean-Marc LINA and Michel MAYRAND
Atlantic Nuclear Services Ltd. and Laboratoire de Physique Nucl'eaire,
Universit'e de Montr'eal, Canada

Using a parametrization of the space of multiresolution analyses with
compact support [-J,J+1] and a maximum of J vanishing moments for the
wavelet, this work investigates the general solution of the orthogonality
conditions. More specifically, all real and complex solutions up to
J=5 are presented. A classification of the well-known real solutions
according to the degree of symmetry of the associated scaling function
is proposed. Furthermore, symmetric but complex multiresolution analyses
are described for a number of vanishing moments up to J=8. Finally, a
symmetric multiresolution analysis is constructed on [0,1].
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