# [LAD] Paul's Extreme Sound Stretch

Robin Gareus robin at gareus.org
Fri Oct 1 01:25:50 UTC 2010

```On Oct 1, 2010, at 2:32 AM, Camilo Polymeris wrote:

>> The original Fourier Transform as invented by the smart French
>> guy of the same name does operate on continuous (as opposed to
>> sampled) data from -inf to +inf.
>
> I understand Fourier invented the Fourier Series "only", anyone knows
> who generalized it to FT?

"Fourier’s initial series lacked the precision of a function, and Dirichlet and Riemann would later express the series as a formal integral." [1]

and

"The first fast Fourier transform (FFT) algorithm for the DFT was discovered around 1805 by Carl Friedrich Gauss.." [2]

[1] http://www.k-grayengineeringeducation.com/blog/index.php/2007/12/21/engineering-education-today-in-history-blog-fourier-series-introduced/

[2] http://en.wikipedia.org/wiki/Fourier_analysis#History

> And yes, I think the FT isn't so hard to understand, and a pretty
> useful concept. FFT, on the other hand... never really tried.
>

Sometimes I regret that I skipped most of the group theory lectures (I still have a very different idea what "group-theory" should be about) but I stopped worrying: libfftw [3] is pretty well documented, comes with a good manual and a tutorial.

Unless you're really into maths and numerics you'll probably learn nothing useful. That might be actually the reason why DFT algorithms have been re-invented or re-discovered  a couple of times during history: 1805, 1965, 1984 [4].
If I may suggest: read up on DFT and leave FFT to the the maths geeks.

[3] http://www.fftw.org/

[4] http://en.wikipedia.org/wiki/Fast_Fourier_transform#Cooley.E2.80.93Tukey_algorithm

Cheers!
robin

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```