The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 6, Issue 5

Question: 3rd order orthogonality?
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Aime' Fournier (

PostPosted: Wed Apr 30, 1997 5:57 pm    
Subject: Question: 3rd order orthogonality?
Reply with quote

#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

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

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



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
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.025439 seconds : 18 queries executed : GZIP compression disabled