[LAD] Paul's Extreme Sound Stretch

[Philipp Überbacher]

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:
> 
> > > 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.

And I guess this is where the windowing comes in. Calculate the spectrum
of small pieces instead.