Say we have mixed three sources, let's call them L (panned hard left), C (center) and R (hard right). Then the left channel has +L+C, and the right channel has +R+C.
Now we phase invert one of them, say the right channel, and combine them. The new mono file is +L+C-R-C. +C-C cancels out and we're left with +L-R.
Since +R and -R essentially sounds the same, it sounds like if we had originally done a mono mix of L and R (+L+R).
But we can't combine this with a straight mono conversion (+L+C+R+C) in any way that will remove both L and R. All we can do is reproduce +L+C or +R+C.
Also if you have the removed data all you have to do is invert it and sum it against hte original material and it will cancel out
I described it slightly incorrectly in the original post but I have used this process to extract vocals for remixing
The first inversion produces one channel containing nothing but stereo data, as you're summing L+Ri to produce S -- the center channel data (technically, anything equivalent in both stereo channels) cancelled itself out. (Note that if you combine L+Ri you should get a zero-ed out waveform)
The second inversion, produced by combining the first inversion (Ri) and the original source converted to mono (L+R), produces the isolated center channel (M). It works because you are essentially only cancelling out stereo data you generated in the first inversion
If you don't believe me, load up a copy of Audacity or Sound Forge and try it. (Note the music needs to be uncompressed) One track this works with is the original mix of "Day n Nite" by "Kid Cudi" if you can find a WAV copy somewhere. It doesn't work with a lot of music
So...
L, R = stereo_split(X)
Ri = inverse(R)
S = L+Ri
Si = inverse(S)
M = Si+(L+R)
Note: L+Ri should result in empty waveformIf you say you have a file where +L-R = 0, then L = R? That’s just a mono file?
L/R stereo and M/S stereo conversion works like this. M = L+R, S = L-R (or S = R-L, either one is fine).
If you expand out your expression M=Si+L+R, where Si=-(L-R)=-L+R, you have M=-L+R+L+R, which means you are saying M=+R+R. This doesn’t seem right.
If you just want an actual M, that’s just a mono conversion of L+R. For sure, if the recording is M/S, the two sides cancel out and you will extract the mid channel, which would often contain song - but there’s no reason to do all the repeated inversion and mixing to do it!
+L+R gets you a mono file (before volume reduction). +L-R cancels out. Try it out in a wave editor with a sine wave
The figures I wrote in my previous post use + as a summing operation, not to signal polarity
I discovered the process on my own, so I'm sure there are better ways to do it, I'm not a recording engineer :)