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   -> Volume 6, Issue 5


Question: 3rd order orthogonality?
 
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Aime' Fournier (fournier@stormy.geology.yale.edu)
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PostPosted: Wed Apr 30, 1997 5:57 pm    
Subject: Question: 3rd order orthogonality?
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#27 Question: 3rd order orthogonality?

Dear Wavelet Creators,

Has anyone designed orthogonal wavelets (Wjk(x)) which are not only
orthogonal wrt scale j & position k:

<Wjk()Wlm()> = delta(j-l)delta(k-m),

but also satisfy prescribed "3rd-order constraints", ie. constraints on

<Wjk()Wlm()Wpq()> ?

Suppose the particular constraint of interest was something like

<Wjk()Wlm()Wlm()> ~ delta(j-l)delta(k-m),

ie. that the basis functions also be orthogonal to each others' squares.
(This would be an attempt at regaining the property

<Fn()Fm()Fm()*> ~ delta(n)

which holds for the Fourier case Fn(x)=exp(inx).)
Well, the constraints above would imply Wjk(x)=const., which is
useless. 

The real question is, what a priori 3rd-order constraints (some other
kind of sparseness) can be usefully imposed on orthogonal wavelets,
besides the recursion relations which hold for dilated-translated type
bases?

Please email me your replies and I'll submit a summary to WD.

Thanks-

Aime'

Aime' Fournier, Yale Univ. Dept. of Geology and Geophysics
PO Box 208109, 210 Whitney Avenue, New Haven CT 06520-8109 USA
tel: 203 432 3146 fax: 203 432 3134
fournier@stormy.geology.yale.edu
All times are GMT + 1 Hour
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