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From: tmb@wheaties.ai.mit.edu (Thomas M. Breuel)
Newsgroups: comp.dsp,sci.math
Subject: Hartley transforms
Keywords: transforms, Hartley, Fourier, FFT, FHT
Message-ID: <9706@life.ai.mit.edu>
Date: 5 Aug 90 00:49:34 GMT
Reply-To: tmb@ai.mit.edu
Followup-To: comp.dsp
Organization: MIT Artificial Intelligence Lab
Lines: 25

Does anyone know or have pointers to the literature or code about how
to do multidimensional Hartley transforms (i.e., is it obvious that a
2D HT is the same as 2 1D HT's, or do I need some correction), and what
the correlation and convolution theorems look like for multidimensional
Hartley transforms?

A straightforward derivation and implementation of the convolution/correlation 
theorems would give 4 times the number of multiplications for a convolution/
correlation as the corresponding (complex) Fourier method and not allow
the operation to be done "in place" (replacing one of the input
arrays). I think by rearranging terms I can fix this, but I would
rather not have to work it out myself.

Also, does anyone have code for the FHT (C/Fortran)? Currently, I am
using a REALFFT routine and re-arrange the output, which is probably
not very inefficient, but not quite as fast as it could be.  Have the
patent issues involving the FHT been resolved?

					Thanks, Thomas.
					tmb@ai.mit.edu

PS: the Hartley transform is a real transform that is
closely related to the Fourier transform and has some
practical advantages over it if all you want to do is
operate on real data.