Over the months, I’ve read a couple of posts asking whether it is possible to 
extract or synthesize surround channels from binaural stereo or non-Ambisonic 
surround formats. I am now attempting to do something that would appear to be 
simpler and more straightforward: that *something* being the conversion of 
conventional L-R stereo to L-C-R.
My reason for wanting to do this is because I have three loudspeakers that I’m 
very fond of: A pair of vintage KRK 7000s and a single KRK 9000 (not with the b 
suffix). I want to use the 9000 as the center channel because it has as the 
same Focal tweeter as the 7000s, but the 9000 has a much larger woofer (the 
7000s being somewhat deficient in this area). I thought it would be fun to 
experiment with a full-range center channel in lieu of using the 9000 (or any 
speaker) as a sub-only.

There’s a lot of info on the Internet about converting stereo to mid-side, but 
not too much about L-C-R. The simplest *fix* would be

C = (L+R)/2

which is akin to extracting the mid signal from a mid-side encoding. But this 
doesn’t separate what is only in the left channel, what is only in the right, 
and what is common to both L + R. If I have a sound going only to the L 
channel, using (L+R)/2 would give me half of that sound on the center channel. 
Needless to say, signal separation would suffer.

Going a step further, the left channel, L, contains the unique part of its 
content, l (lower case L), and half what is common, or C/2. That is,

L = l+C/2

Likewise:

R = r+C/2

But to extract what is common in terms of R and L is algebraically impossible 
because we don’t know what l and r are (l and r don’t cancel out); I suppose if 
we did, then there wouldn’t be a problem to begin with. The problem doesn’t 
exist when you have stems to work with (e.g. cinema sound track production) in 
lieu of attempting to extract it from existing L and R channels.

Perhaps this simple exercise also explains, at least in part, why we can’t 
derive Ambisonic channels from non-Ambisonic sources (mathematically, it seems 
impossible to set up a determinant with unique solutions).

Perhaps readers here have had success with a simple stereo to L-C-R converter? 
I have converted Ambisonic recordings to L-C-R: This is pretty easy with any 
number of plug-ins (I use Harpex for most of my Ambisonic processing).
Thanks for everyone’s time.
Best,
Eric C.
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