music editing / decomposition

Juan M Vuletich jmvsqueak at uolsinectis.com.ar
Mon Sep 22 02:45:57 UTC 2003


On Thu, 18 Sep 2003 20:58:45 -0400, Joshua 'Schwa' Gargus wrote:

>On Thu, Sep 18, 2003 at 07:51:04PM -0400, Juan M Vuletich wrote:
>> Hi,
>> 
>
>> A FFT (actually a you need a windowed Fourier transform) won't have
>> enough joint time and frequency resolution at both high an low
>> frequencies.  A continuous wavelet transform could be used for the
>> analysis, 
>
>How does a continuous wavelet transform differ from a discrete one?
>I'm only familiar with the latter.
>
They are almost unrelated. The continuous wavelet transform takes the wavelet function, at every real dilation (or scale) and real displacement and for 
each scale/time pair it takes the correlation between the function being transformed and the wavelet. Using a complex Morlet wavelet (a modulated 
Gaussian) and a fine sampling of the time - frequency plane you can get a very good measure of the time/frequency energy content of a signal.

>> but it can't reconstruct signals, so it can't be used if
>> you want to rebuild the different sounds. A discrete wavelet
>> transform won't have enough frequency resolution. So, it's an open
>> problem, and there is currently a lot on research on it. This very
>> problem has been my obsession for the last couple of years, and I
>> have just presented a paper with new results on August at the SPIE's
>> Wavelets-X conference in San Diego. (I can send the pdf file to any
>> interested.)
>
>Me, please.
>
I'm sending it in a different mail, to avoid sending a big mail to the list.

>> Of course, this is just the analysis and reconstruction of the
>> signals, in middle you need some sort of AI, fuzzy logic, neural
>> nets or such to do the actual separation of the sounds.
>
>Hm, interesting.  What would your training set consist of?  Pairs
>of multi-track music clips and a single track from the same clip?
>
I've never thought of that, it's a great idea!

>Hopefully I'll have smarter questions to ask once I've read your
>paper. :-)
>
Cheers,
Juan



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