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   -> Volume 5, Issue 6


Question: Implementation of Mallat algorithm
 
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Andy Woodward (azw@aber.ac.uk)
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PostPosted: Fri Aug 09, 1996 1:37 pm    
Subject: Question: Implementation of Mallat algorithm
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Question: Implementation of Mallat algorithm

Something has been confusing me about some implementations of the
Mallat algorithm.

The big advantage of the Wavelet Transform over the FFT is its ability
to deal with non-stationary signals. In some versions of the Mallat
algorithm, the filter ladder is implemented in the frequency domain
relying on the Convolution Theorem (that a convolution in the time
domain, as carried out by a Toeplitz-like matrix, is equivalent to a
multiplication in the frequency domain). BUT in order to transform to
the frequency domain to carry out this procedure, an assumption must
be made that the data at that scale is stationary or one of the
fundamental assumptions of the FFT (and hence of the Convolution
Theorem) is violated. So it seems to me that the wavelet pcoefficients
calculated in this way must reject the nonstationarity that is one of
the main reasons for using the WT in the first place?

I assume I am misunderstanding something fundamental here - what????

Is it valid to calculate the Mallat algorithm in the frequency
domain, or only (as it seems to me) exclusively in the time domain?
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