Re: revised version of wavelet transform

[Brian Gough <bjg at network-theory dot co dot uk>]

Ivo Alxneit writes:
 > i dont think that this is really usefull. maybe your thought comes
 > from the fact that the "size_t n" in gsl_wavelet_alloc() is really
 > the member selected. this CAN BE the number of coefficients (haar,
 > daubechies) or just an acronym (bspline, 204 means 2,4 spline of
 > the original publication). i did implement all members of those
 > families that were given in the original publication. so it is not
 > like e.g. in some special functions where the implementation only
 > works for a certain sub-range of an argument.

Ok sounds like it is not useful.  Also the FFT doesn't have it either.

 > the current implementation results in h_ping.ps because the
 > wavelets are not centered i.e. the position on the wavelet is
 > associated with its trailing (left) edge. this is the way all
 > implementations i checked work. if you center the wavelet i.e. its
 > position is associated with its center and you will obtain the
 > easier-to-read heisenberg box plot (h_ping-c.ps).  leaving the
 > choice (centered/not centered) to the user is easy to implement: 1)
 > add a boolean to the gsl_wavelet structure.  2) allocate according
 > to gsl_wavelet_allocate (family, member, centered/not-centered).
 > 3) add if(centered) nmod -= (w->nc >>1) in gsl_dwt_step().
 > or (instead of 1 and 2 above) add a parameter to the different calls 
 > gsl_dwt_....(..., centered/not centered) 
 > should i add this ? i prefer the second solution

Is it possible to do it using the gsl_wavelet_type struct?
e.g. gsl_wavelet_bspline and gsl_wavelet_bspline_centered
That seems quite natural.

-- 
Brian Gough