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   -> Volume 3, Issue 7


Question: Derivatives of Daubechies wavelets
 
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Alistair Rowe (arowe@tartarus.uwa.edu.au)
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PostPosted: Mon Dec 02, 2002 1:01 pm    
Subject: Question: Derivatives of Daubechies wavelets
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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.
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