Someone asked this on another forum I'm on, and I'm pretty curious about it myself so I'm relaying it here since this is specifically a sound/audio based site.
But anyway, if we define a stereo sound as being:
L+C on one channel, and R+C on the other, where
L = information unique to the left side
R = information unique to the right side
C = information common to both channel (center)
Adding the two channels gives L + R + 2C
Also, subtracting them gives L-R or R-L, effectively getting rid of anything center-panned (most people know about this as a way for removing vocals from a song).
So now, the real question. Is there any way to get C by itself? That is, isolating anything that is centered, getting rid of anything unique to the left or right channel. I can't think of any way that would be possible without using the fourier transform, but I keep thinking I'm overlooking some clever manipulation that would allow extracting just the center panned sounds. In the frequency domain, it would be pretty easy to just pick out the components that are the same amplitude/phase in both channels, but anyone have any idea as for how it could be done strictly in the time domain?
Centre pan isolation is not possible using the inversion technique, only centre pan removal is possible using inversion (destructive intereference) method.
There are free centre pan isolation plugins ... http://www.freesound.org/forum/viewtopic.php?t=5899
The paid for version of Extraboy* ($30) does a fair job but still has digital artifacts.
To misquote Dr Johnson,
centre pan extraction is like a dog walking on his hind legs. It is not done well; but you are surprised to find it done at all.
Something like this is done in Dolby Pro Logic systems, although for that to work properly, the sound has to be encoded by a Pro Logic encoder. But then it does split a stereo track into four (left, right, center, surround) tracks. And even then, it's not perfect. If one would use, for example, MS recordings in this system, you're likely to find some of this material in the surround rather than on left and right, because of the inverted phase.