30 Sep
2010
30 Sep
'10
1:53 p.m.
On 09/30/10 13:15, Dave Phillips wrote:
Robin Gareus wrote:
LOL.
basically, Fourier proved that any signal can be represented a sum of
sine-waves.
(well, that's not entirely true: it needs to be a periodic signal, but
the period length can approach infinity...)
FFT is "just" the implementation of that theorem (or Principle?!)
In layman terms:
There's a smart French guy by the name of Joseph F. sitting inside it:
If you play him some audio: He thinks: "Hey, this is actually just a few
simple sine-waves added together (superpositioned)", he quickly
calculates their frequencies and amplitudes and asks "Now, you want to
change the duration?" easy: "I'll generate some new sine-waves with
these frequencies and amplitudes, how long did you say you want?"
(The smart thing about this French guy is that he actually speaks fluent
English - Sorry I could not resist :)
I recall a brief exchange on a DSP list that went something like this:
Q: Can anyone explain the FFT in simple terms ?
A. No. I have read and understood some articles and
descriptions of the FFT.
Mark Dolson's original article on the phase vocoder (in the Computer
Music Journal V10,#4, Winter 1986), is still a good introduction for
computer-based musicians, though it may be a bit too technical by
contemporary standards.
Louigi, take a look at some descriptions of what an FFT does. It does
use "windows" but you'll have to do some homework to find out what's
meant by the term in this context.
http://en.wikipedia.org/wiki/FFT
Beware, that page is a maths page, it's not directly concerned with the
use of the FFT in music/sound applications.
It may help to make some connection with the equations on
http://en.wikipedia.org/wiki/Fourier_transform if you know that
sin (x) = ImaginaryPartOf ( e^(i x) )
cos (x) = RealPartOf ( e^(i x) )
where i = sqrt(-1);
And btw, I agree wrt Paul's Extreme Stretch,
it's a great tool.
It is indeed. Kudos to Paul.
FWIW, http://arss.sourceforge.net/ works similarly. It provides
sound-to-image and image-to-sound functionality using FFT.
You can also use it to do time-stretching but it's actually more fun to
toy around with it: http://arss.sourceforge.net/examples.shtml
Best,
dp
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