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

# Choosing an appropriate wavelet basis

Started by ●May 21, 2008

Reply by ●May 22, 20082008-05-22