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Characterizing wavelet spectra

Started by Andreas Steffen April 24, 2007
Hello!

I'm trying to classify situations by their wavelet spectra, and I'm
looking for a good way to characterize each spectrum. What ways are
there to extract a small number of characteristic values from a large
multiscale analysis result that allow recognizing similar situations?

Thanks
Andreas Steffen
Andreas Steffen wrote:
> Hello! > > I'm trying to classify situations by their wavelet spectra, and I'm > looking for a good way to characterize each spectrum. What ways are > there to extract a small number of characteristic values from a large > multiscale analysis result that allow recognizing similar situations?
That depends. What characterizes your situations? Regards, Andor
Hello there,

> I'm trying to classify situations by their wavelet spectra, and I'm > looking for a good way to characterize each spectrum. What ways are > there to extract a small number of characteristic values from a large > multiscale analysis result that allow recognizing similar situations?
Wavelet decompositions (and other transforms in general) are typically used to attain good sparsity in the transform spectrum, i.e. having *most* of the signal energy in as few as possible high magnitude coefficients. Depending on your situation, you can take advantage of this fact and represent classes of signals by their "representative" high magnitude coefficients. Also, if you use a dyadic wavelet transformation, you obtain multiresolution approximations and detail coefficients. In typical situations, the approximation ones are all preserved (and in case of full-dyadic decomposition, there is only one approximation coefficient, the DC coefficient). Kostadin