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, 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.)

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.

Cheers,
Juan

On Thu, 18 Sep 2003 14:18:21 -0500, Daniel Joyce wrote:

>On Thursday 18 September 2003 11:40, Gary McGovern wrote:
>> Thanks for all those links and resources. I'm more than surprised this
>> isn't more evolved. I thought if the human ear could selectively pick out a
>> track in a composition / song then that track has its own unique state and
>> behavior and it would just be a matter of defining the state and behavior
>> and identifying those tracks electronically.
>>
>> Thanks again.
>>
>> Gary
>>
>
>The problem is, music is the sum of all the frequency, harmonics, and phase 
>information in it.
>
>If I give you the number 100, can you tell what numbers I summed or multiplied 
>to arrive at that number? 100x1? 20x5? 4x20+20? It's impossible to tell, the 
>information is lost in the process. :)
>
>Now with music, that isn't entirely true. But, yer gonna need to do some work. 
>You're probably going to need to work in the Frequency domain ( so use a FFT, 
>or wavelet transform to get there ), and also, phase information ( a bit more 
>trickier ). Once you've got all that, it might be possible ( depending on 
>signal noise, etc ) to pick out one trumpet, and 'follow' it through the 
>piece. You KNOW what a trumpet sounds like, but how do you tell the computer 
>that? ( Possibly, take a trumpet sample, and have it scan for a 'closest' 
>match in some fashion ).
>
>Turns out, the reason why it's easy for people to do it, to hear and follow 
>the trumpet piece in the symphony, is that some of the work is done by the 
>structure of the inner ear ( Different frequencies excite different areas of 
>the spiral shaped inner ear, so in essence, it's performing a Fourier 
>transform ), and the brain is a massively parallel machine. 
>
>
>The Meek shall inherit the Earth,
>for the Brave are among the Stars!
>
>