[Help-gsl] 2d FFTs, DCTs, etc.

[Dimitris Papavasiliou]

Hello all,
I needed to perform a 2D DCT for image processing and since speed wasn't 
such an absolutely critical issue (although welcome of course) I thought 
I'd implement it using GSL instead of FFTW.  In the spirit of unifying 
all our numerical needs (which the GSL seems to be serving well enough) 
under a common interface I thought I'd implement this as a GSL package 
as well which might later be incorporated into GSL itself.

Until now I have basically only radix2 DCTs (type II and inverse which 
is essentially type III) implemented for one and two dimensions.  I also 
created a couple of wrappers for the FFT functions that work with 
vectors and matrices.

Now what I'm interested in is the following:
a) Is there an interest in such a package (1D, 2D, DCTs, 2D FFTs maybe 
and vector/matrix interfaces for the lot) or should I just implement 
DCTs for myself?  I'm asking because these things are easy enough to 
implement that I thought there might be a reason why they aren't 
provided by the GSL yet.
b) Is there a reason why there are no vector/matrix interfaces to the 
fft functions (in constrast to the wavelets routines)?
c) Is there a reason why there are no two-dimensional fft routines?  For 
real data there would be the problem of computing them in-place I 
suppose but for complex data computation is pretty simple using 
row-column decomposition.

In case there is an interest in such a package, does anyone have any 
ideas on the following:
a) What to do with 2D real FFTs?  In-place computation (without 
allocating extra memory) should be impossible ,at least using 1D FFTs to 
do the job.  Should only complex 2D FFTs be implemented?  Should real 
FFTs have different input and output vectors (that would break the 
symmetry in the interface though)?
b) Does anybody know whether it is possible to compute DCTs of odd 
length using one FFT of the same length?  For even lengths this is 
possible (both powers of two and not) but for odd lengths I haven't 
found anything.
c) Would anyone be willing to help out (esp. with the vector/matrix 
wrappers and with making these work for doubles and floats through those 
GSL templates)?  I'm supposed to be doing my master's thesis as well 
(what I needed the DCT for in the first place) so it might take some 
time to finish this on my own.

Sorry for all the questions,
Dimtiris P.