Re: fft and wavelets

[Rudolf Widmer-Schnidrig]

On 23.08.12 11:32, Sergei Steshenko wrote:
> --- On Wed, 8/22/12, Rick T <address@hidden> wrote:
>
> From: Rick T <address@hidden>
> Subject: fft and wavelets
> To: address@hidden
> Date: Wednesday, August 22, 2012, 7:21 PM
>
> Greetings All
>
> I can use fft to get the, frequencies, phases and magnitude of a loaded 1 second audio 
> file of person saying "ahhhh" and recreate it.
> What I'm trying to do now is find out where each of those frequencies begin and 
> where they stop in the 1 second audio file
>
>
>
> Example:100hz starts at .23seconds to .34seconds,
> 104.34hz starts at .35seconds and ends at .37seconds.
>
> Can fft's do this or do I need to shift my whole program to use wavelets?  Also 
> are there any wavelet examples in octave that show how do this?
>
>
>
> I'm using Ubuntu Linux 12.04 and Octave 3.2.4 from the repo's
>
> Thanks
> Rick
>
>
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>
> http://www.gnu.org/software/octave/doc/interpreter/Signal-Processing.html#doc-fft 
> -> stft (short time Fourier transform).
>
>
> Regards,
>    Sergei.
>
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Dear Sergei,

what you are trying to do violates the uncertainty principle of the 
Fourier transform.
This uncertainty principle states that the product of the resolution in 
the time domain and the frequency domain is some constant. If you 
increase one you necessarily decrease the other.

Short time Fourier transforms and wavelets are just different ways of 
making a compromise between the two end member cases of perfect time 
resolution that you have in the time series and the perfect frequency 
resolution that you have in the Fourier spectrum.

                          -Ruedi