Talk:Discrete Hartley transform

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A+ effort on this topic. Excellent job! --PY

I agree -- I've been too lazy to put in scholarly references. Or maybe too responsible: I have work to do; God only knows why I work on this stuff instead. By probably I'll put a few references at binomial type. Michael Hardy 01:47 Apr 8, 2003 (UTC)


This is bound to be an extremely stupid question. Well here goes nothing...

If the inventor of these mathematic thingamagics is called Bracewell, howcome they aren't called frex. "Discrete Bracewell transform" etc.? Where does the name "Hartley" enter into the subject? I'm probably just stupid, but maybe the article too could benefit from a short reference to the origin of the name. -- Cimon Avaro on a pogo-stick 19:23 21 Jul 2003 (UTC)


I thought it was clear: Hartley invented the continuous transform, just as Fourier invented the continuous Fourier transform (the discrete version came later, or earlier if you count Gauss, although Gauss apparently thought of it more as a fit than as an invertible transform). Actually, Bracewell initially did try calling it the Discrete Bracewell Transform in his patent application, but that apparently didn't fly: in science you generally don't get to name anything after yourself. So, by the time he published his first article on it, he was already calling it the Discrete Hartley Transform; it would be interesting to hear what convinced him to change (second thoughts? colleagues? referees?), but I don't know the story. Steven G. Johnson

Well, my first comment about it being a stupid question still stands :)

It isn't really here nor there, and definitely not specifically directed at this article in particular, or even just maths in particular, but sometimes I just get the feeling there is some history behind things which everybody who is an expert knows about, and secretly smiles at... Maybe some of the articles I have contributed to may seem that way to others too... Just was something I was curious about. But thinking back on it, maybe it isn't important enough to add to the article. -- Cimon Avaro on a pogo-stick 20:23 21 Jul 2003 (UTC)

Note the article you mention was published in 1983, and the patent applied for in 1984. Bracewell called it the fast Hartley Transform in advance of the patent application, which did fly, since the patent was granted with the title ... discrete Bracewell Transform. Bracewell didn't "try calling it" anything in "his patent application". Stanford University made the application and the title thereof. Bracewell always called it after Hartley, before and since, and that's probably why it's known by that moniker. OK, so maybe I should recuse myself from the issue because of a bias, but frankly, he's a nice guy, very smart, a great Dad, and he did the work after all. -- Mark C. Bracewell

Thanks for letting us know the personal story that Prof. Bracewell wasn't behind the name in the patent application. (This is unusual; in my experience with scientific patents, patent attorneys typically make only cosmetic changes and don't alter technical terms in the patent description, which is usually submitted to them in draft form by the inventors and not by the institution.) As for the dates, I had assumed that the patent text dated from an earlier disclosure or provisional filed by Bracewell prior to publication & filing, which is the usual practice these days (not filing anything until after publication loses you international patent rights), but I guess that wasn't the case here. Actually, I checked the dates and I had miscopied one of the references anyway (now corrected). Steven G. Johnson 02:37, 24 Oct 2003 (UTC)
By the way, it's not really a criticism of your father to suggest that he wanted something named after himself—many people in science do—you just can't do it in the most straightforward way (patent applications don't count, since the patent examiners don't care what you call it). (A professor of mine once advised me: if you come up with something important, don't give it a sensible name; that way, people will be forced to use your name to refer to it.) Sorry if I came off sounding snide. Steven G. Johnson

Likewise - sorry if I came off sounding offended. ...don't give it a sensible name...—would that account for the FFTW? I don't doubt that it's the fastest, but MIT is in the east. -- Mark

It's not in the East if you have an Italian co-author.  :-) It's also too sensible according to my professor's theory, since it is a catchy name that everyone remembers. His advice would probably have been something unwieldy like, "An adaptive system of composable units for implementing fast Fourier transform algorithms." —Steven G. Johnson

Fourier-Hartley correspondence[edit]

FYI - Additional section on Fourier-Hartley Correspondence posted on behalf of Dr. Bracewell, as I'm the one in the family that speaks wiki. -- Mark C. Bracewell

Thanks Mark. However, I'm forced to remove it for the time being. Much of what you posted is more suited for Hartley transform and/or is redundant.
Note that the article already says how to get the DFT from the DHT, and how the convolution theorem works for the DHT. The article already deals with the operation counts as compared to the DFT, and frankly I found the text you posted to be a bit misleading in claiming that the DHT halves the operation count. (As far as is currently known, the DHT has no inherent advantage in arithmetic over an FFT specialized for real inputs, at least for composite sizes, and the latter is at least theoretically slightly more efficient.)
The information about optical Hartley transforms is interesting, but belongs in Hartley transform not here. (Note that optical Fourier transforms that preserve phase information also exist. I would be interested to learn whether anyone uses the optical Hartley transform any more in practice, as I can't find any citations of the 1987/88 Villasenor & Bracewell papers in the last 10 years.)
If you do add information to Hartley transform, please make an effort to use the same notation as in that article, and to avoid adding redundant information—integrate your additions with the article! —Steven G. Johnson 07:53, 2 May 2006 (UTC)
—Steven G. Johnson 07:47, 2 May 2006 (UTC)