linuxaudio.org

On 09/30/10 20:49, Philipp Überbacher wrote:

quoted text
> 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

quoted text
>> 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

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