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 3, Issue 9

Question: A proper grid for locating orthogonal wavelets ...
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Ali Akbar Safavi (

PostPosted: Mon Dec 02, 2002 1:08 pm    
Subject: Question: A proper grid for locating orthogonal wavelets ...
Reply with quote

Question: A proper grid for locating orthogonal wavelets ...

Question: A proper grid for locating orthogonal wavelets of different
scales in a multi-resolution approximation :

Dear Wavelet-ers

I follow Mallat's work on " A Theory for Multi-Resolution Signal Representation:
The Wavelet Representation "
and publishied in : IEEE Trans. on pattern Analysis and... (1989).
I have a question and appreciate your comments.

My Question is:
If we construct a grid (whose interval in proportional to 2^(-j))
for locating wavelets at different scales,
then, should the wavelets at one scale be orthogonal to all the
wavelets of the other scales, in orther to have a multi-resolution
analysis without redundant information in our detail (the difference
between approximation at two different scales)?
1. the orthogonality of translation of wavelets for each
particular scale is satisfied;
2. we only look at orthogonal wavelets;
3. the wavelet may be centered at t=0 or t=1/2; )

A negative answer accept the two following grids, while a positive answer accept
only the first grid,
(First) finest res. * * * *
* * *
* *
coarsest res. *

(Second) finest res. * * * * *
* * *
coarsest res. * *

The grid that Daubechies uses in page 10-11 of "ten lectures on wavelets"
to give an example of multi-resolution with Haar wavelet is the same as
the first grid. Moreover, in that example she proves orthogonality of Haar
wavelets of all different scales.

Best regards

akbar safavi
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.024221 seconds : 18 queries executed : GZIP compression disabled