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Choosing an appropriate wavelet basis

Started by Unknown May 21, 2008
I have been spending some time learning about and implementing
wavelets, but there is still one lingering question that I have:

How do you go about choosing the best wavelet basis given a priori
knowledge of the exact signal you are applying it to?

In my particular case, I have what looks like a single Gaussian
enveloped sinusoid of a particular bandwidth and center frequency.
This "pulse" is then replicated, shifted, and placed next to the
original pulse to yield a two dimensional image looking something like
this ( a sinusoid in the vertical dimension and shifted versions of
the same sinusoid in the horizontal dimension):

          _   _
     _   _   _   _
_   _   _   _   _   _
_   _             _   _
_                      _


I would imagine that the best basis for a transformation along the
vertical dimension would be the Gaussian enveloped sinusoid itself,
no?  If my wavelet and my signal exactly match at a specific scale,
this would mean that there would be a single coefficient at a single
scale and all else would be zeros, right?  How do I go about find the
appropriate high pass and low pass analysis and synthesis filters for
this data?  Furthermore, if I wanted to do the compression in 2D,
would it make sense to use a different basis for the horizontal
dimension than I use for the vertical dimension?  Is this even
possible?

Thanks for your time,
Mike
Assuming those are time series samples, from a low-frequency standpoint
that looks very similar to a Daubechies mother wavelet.

Mark