30 Sep
2010
30 Sep
'10
9:23 p.m.
On 09/30/10 20:49, Philipp Überbacher wrote:
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
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.