30 Sep
2010
30 Sep
'10
8:49 p.m.
Excerpts from fons's message of 2010-09-30 14:29:01 +0200:
On Thu, Sep 30, 2010 at 01:53:44PM +0200, Robin Gareus
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. The 'spectrum' interpretation
came later. It was originally a mathematical tool used to find
integrals of functions that would be impossible to integrate in
closed form, and Fourier himself used it to study the propagation
of heat in solids.
The DFT (Discrete FT) is the same thing operating on sampled
signals. It is usually also limited in time.
The FFT (Fast FT) is an algorithm to compute a finite-length
DFT very efficiently.
The 'spectrum' interpretation is really quite ambiguous.
You could take the DFT of e.g. a complete Beethoven symphony.
The result is the 'spectrum' and in theory this is fixed over
infinite time - the frequencies that are present according to
this spectrum are there *all the time*. But that is not how
we would perceive the music - we do not hear a constant mash
of all frequencies, the spectrum as we hear it changes over
time.
Ciao,
--
FA
There are three of them, and Alleline.
And I guess this is where the windowing comes in. Calculate the spectrum
of small pieces instead.
Q: Can
anyone explain the FFT in simple terms ?
A. No.
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?!)