There is considerable  legalities  concerning  the  use  of the Fast
Hartley Transform.  (The FHT is very similar to the FFT.)

It appeares that Bracewell has somehow managed to  claim  patent  on
the  entire  FHT concept.  Not just a particular implementation, but
the  entire  concept  of  doing  a  'Fast'  version  of  the Hartley
Transform.  That's quite a stretch considering the Hartley transform
was developed 50 years ago, and the tehcniques to split that type of
transform (ie:  the Fourier Transform) into the 'Fast' variety  were
developed  30  years ago (Cooley, etc.) and possibly even far before
that (Gauss).

For the record, I developed my FHT code directly  from  a  recursive
Fast  Fourier  program and the Hartley mathematical formula.  It was
almost a straight, simple  conversion  to  the FHT program simply by
replacing the complex function with Harltey's 'cas' function.

However, as I am in absolutely  no  financial  position  to  legally
challenge Bracewell (note no 'Mr.' in front of his name as a sign of
respect....!   I  have  a strong opinion of people who file software
/ mathematical patents) or his patent, that code may or may not fall
under  his  legal patents.  (I think somebody needs to have a rather
forceful conversation with him  and  teach  him that mathematics and
patents don't go together!  Perhaps fill your mouth with cotten  and
make  him  "an  offer  he  can't refuse"<g> (For you foreign people,
that's a reference to the movie "Godfather", with Brando).)

So, the use of  this  function  may  or  may  not fall under various
legalities.


I'll  flatly  state  that  I don't like including the FHT due to the
legalities.  I  strongly  disaprove  of  software patents.  However,
after some rather insistent comments  by a beta tester, I've decided
that I might as well.  The whole purpose of v2.3 was  'for  others',
so, I might as well.


This is the only information I have on the software patent, although
I have no doubt as to its accuracy.

The patent was granted in 1987, so it will expire in 2004.


The Fast Hartley Transform algorithm  is covered under United States
Patent Number 4,646,256.  Implementations may  be  freely  used  and
distributed only under the following conditions:

      1) This information is included in every copy of the code; and

      2) The code is used for non-commercial research purposes only.

Firms  using  this code for commercial purposes will be infringing a
United States patent and should contact the:

            Office of Technology Licensing
            Stanford University
            857 Serra Street, 2nd Floor
            Stanford, CA 94305-6225
            (415) 723 0651





