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   -> Volume 4, Issue 4


Question: spectrum of wavelet opertors
 
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Jean-Philippe Brunet
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PostPosted: Mon Dec 02, 2002 6:07 pm    
Subject: Question: spectrum of wavelet opertors
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Question: spectrum of wavelet opertors


What is known about the spectrum of wavelet operators?

The spectrum of the Fourier transform operator is uniformely distributed on
the unit circle. I am curious as to what is the distribution of eigenvalues
for a wavelet transform operator, in particular whether it would have a
fractal character. I tried a few keyword searches in the Wavelet digest but
I thought I would ask you directly.
Regards,


Jean-Philippe brunet
Thinking Machines Corporation
245 First Street
Cambridge, MA 02142


I computed the eigenvalues of the
discrete wavelet transform matrix (DAUB4) of moderate size (N=1000). The
distribution on the unit circle is non uniform, but that's all I can really
say.
If one were to relax the orthogonality constraint then the
eigenvalues will spread over the complex plane, perhaps showing interesting
(fractal?) patterns (but are there non othogonal wavelet operators of
practical interest?). Before I spend some time on this I was curious of what
had been done.
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