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From: Greg Heath <heath@alumni.brown.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Hilbert Transform
Date: Wed, 14 May 2008 08:07:38 -0700 (PDT)
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On May 9, 6:46=A0pm, "Steven G. Johnson" <stev...@alum.mit.edu> wrote:
> 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). =A0Cooley 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=3D1162257).
>
> 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. =A0But I thought I should correct the record.
>
> Regards,
> Steven G. Johnson

Another offtopic bit. PreCooley-Tukey we were simulating electron
beams, plasmas and spiral galaxies by solving Poisson's Equation
on a 48X48 grid using a 3X2^4 FFT. I think the computer was an
IBM 7070 and each simulation took ~4hrs of clock time. It would
probably take minutes on the average modern day PC.

Greg