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.

> 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.

> 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?

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

> 
> 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.

And similarly that if the human visual system can infer shape
information from the the shading of an object, then getting a computer
to do the same would just be a matter of... ;-)

People are very good at doing some very hard things. (no pedantry intended :-)

Joshua





> >>
> >> 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!
> >
> >
> 
>