> On Thu, Sep 30, 2010 at 01:53:44PM +0200, Robin Gareus wrote:

>

> > > 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?!)

>

> 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.