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 7

Question: Derivatives of Daubechies wavelets
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Alistair Rowe (

PostPosted: Mon Dec 02, 2002 1:01 pm    
Subject: Question: Derivatives of Daubechies wavelets
Reply with quote

Question: Derivatives of Daubechies wavelets

Dear Waveletters,

Dr Paul Abbott and myself have been looking into the so called 'dilational'
derivatives of wavelets such as the Daubechies 4 and Daubechies 6 wavelets.

In truth, the derivatives are of the scaling functions for these cases.

I refer you to Strang Vol 31 No 4 pp614-627, 1989 SAIM Review. He discusses
the connection between the eigenvalues of a system of variables that
correspond to the scaling function values at points within domain of the
scaling function, with the dilational derivatives.

In particular, he says that the first dilational derivative corresponds to
an eigenvalue of 0.5, the second with 0.25 and so on.......

In solving the eigensystem (say for Daubechies 6) we found eigenvalues of
1 (the function), 0.5 (the first derivative), 0.25 (the second derivative),
and another of approximate value -0.27 - What does this correspond to?

Perhaps some sort of fractional derivative?

Alistair Rowe.
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.025607 seconds : 18 queries executed : GZIP compression disabled