On 09/30/10 20:49, Philipp Überbacher wrote: > 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.
Thanks a lot for this comprehensive history lesson. Back when I was introduced to FT in some Physics lecture I was happy that I was able to use it and completely forgot to check the history :) Probably related to why I favored experimental Physics over Theory. >> 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. > correct. Furthermore there are different kind of windows (here a window refers to a block of audio-samples) and windows can overlap. That's where it gets complicated. The most commonly known window shapes are Rectangular window, Gaussian , Hann- and Hamming windows (the last two are cosine shapes) which allow to avoid discontinuities when processing blocks. Cheers! robin _______________________________________________ Linux-audio-dev mailing list [email protected] http://lists.linuxaudio.org/listinfo/linux-audio-dev
