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From: "Steven G. Johnson" <stevenj@alum.mit.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Hilbert Transform
Date: Fri, 9 May 2008 15:46:08 -0700 (PDT)
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On May 9, 1:09 am, Greg Heath <he...@alumni.brown.edu> wrote:
> On May 8, 4:34 pm, "Andy Robb" <ajr...@hotmail.com> wrote:
>
> > "David Egger" <egg...@sbox.tugraz.at> wrote in message
> > Cooley-Tukey invented the modern FFT
>
> No. Cooley-Tukey made the technique known to a wider
> audience.
>
> Oscar Buneman ( a German mathematician at Cambridge who
> was interred by the British during WWII) used it during his
> research for the allies on computer simulations of the radar
> magnetron. He was the first to understand the inner workings
> of the magnetron that allowed British radars to become practical.

Actually, the Cooley-Tukey algorithm's earliest discoverer seems to be
Gauss, who described the technique (including the general composite-N
case) in his notebooks circa 1805.

Subsequently, various forms of the algorithm were rediscovered
multiple times by multiple authors (usually restricted to special
cases like powers of 2).  Cooley and Tukey rediscovered it yet again
in 1965 (including the general composite case), but deserve some
credit not only for popularizing it but also for describing it clearly
and identifying the O(N log N) complexity (which was not clearly
analyzed by most, and perhaps all, previous authors).

There was a nice article, "Gauss and the History of the Fast Fourier
Transform," in 1984 by Heideman et al. that goes over a lot of this
history (http://ieeexplore.ieee.org/xpls/abs_all.jsp?
arnumber=1162257).

Of course, this is a bit offtopic to the original poster, who is
interested in the history of the application of the FFT to Hilbert
transforms apparently.  But I thought I should correct the record.

Regards,
Steven G. Johnson