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convolution

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1943] convolution
• From: Mark Irvine <irvine%bordeaux at christensen.cybernetics.net>
• Date: Sat, 26 Aug 1995 00:08:21 -0400
• Organization: CRIBX1 , Universite de Bordeaux I , France

Dear All

I have a problem calculating or rather normalising wavelet transforms 
calculated via convolution as opposed to the Fast wavelet method.  It 
should be possible to conserve variance under the scale curve when 
properly normalised.

Does anyone have a short notebook with the normalisation ?  or Perhaps 
suggestions as to my problem ?
Briefly my method is to have say 1024 points data and 1024 point wavelets 
(zeropadded) before convolution I normalise the wavelet variance to 1 then 
convolute the standard way as in the book of Wolfram. After that I sum 
each scale and normalise as prescribed to form an 'energy spectra' 
However my results are not the same as the variance.  Note I have not 
forgotten the wavelet constant.

Thanks for your time. Any help is appreciated.
Best wishes
Mark