[music-dsp] time representation in the frequency domain

Dylan Menzies music-dsp at zenprobe.com
Thu May 14 07:50:41 EDT 2009


Jan,

You nearly answered this yourself I think, but the time isn't simply in a 
single phase of freq rep. A delta in time is represented in frequency by a 
infinitely wide spread of frequencies (or finite if sampled) with precise 
phase relationships. Mess with the phases and you have white noise.

Dylan


> ----- Original Message ----- From: "Jan Baumgart" <raga.raga at gmx.de>
> To: <music-dsp at music.columbia.edu>
> Sent: Thursday, May 14, 2009 8:38 PM
> Subject: [music-dsp] time representation in the frequency domain
>
>
>> Hallo!
>> 
>> I've got a mathematical question:
>> When doing a fulltime fourier transform (only _one_ big "frame"), how is 
>> the time information encoded into the phase?
>> 
>> When doing an inverse transform (or for example convolve with an dirac 
>> impulse) you get back exactly the same you put in in the first place. So 
>> the time information has got to be hidden somewhere in the frequency 
>> domain, doesn't it?
>> 
>> When looking at a time domain signal from a fourier view, you can look at 
>> the frequency information as "encoded" as sine function components. Does 
>> the same apply for the time information encoded into the frequency domain?
>> 
>> This seems quite mysterious to me...has there been anything published on 
>> this subject?
>> 
>> cheers,
>> jan baumgart.
>> 
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