Re: [LAD] Paul's Extreme Sound Stretch

On Thursday 30 September 2010 23:16:32 fons@email-addr-hidden wrote:
> On Thu, Sep 30, 2010 at 09:23:08PM +0200, Robin Gareus wrote:
> > 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.
>
> If you're still living in Paris, make sure to visit the 'Musée des
> Arts et Métiers' one day. Quite a nice place for vintage experimental
> physics. It's also the place where the final mad scene of Umberto Eco's
> novel "Foucault's Pendulum" is situated. The pendulum itself used to be
> there, but it's now at the Panthéon.
>
> > > 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.
>
> Even windows won't save you from apparent madness. Imagine a signal
> consisting of all zero samples, except one every second which has
> value 1. Such a signal contains all frequencies that are a multiple
> of 1 Hz, up to half the sample frequency. Those frequencies are present
> all the time. Now take a window of say half a second. If it includes a
> pulse you get more or less the same spectrum again. If it doesn't, you
> get nothing... even if the frequencies should be there :-)

And if I remember correctly, the minimum frequency you get is double your
window-width. So when you do smaller windows like a jack-buffer of 128 samples
at 48kHz, you only get down to 187.5 Hz... You can however overcome this if
you run a second much bigger window where you only extract the low
frequencies.

(Unless Fons corrects me on that...)

Have fun,

Arnold

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