For Dolby Pro Logic Matrix decoding read my posting
BeSweet & Dolby Surround II Matrix
You'll not find much detailed information about DPL2 because Dolby handles it as company secret.
In
Pro Logic II we set the amount of
acoustic power of Rs (right surround) in Lt (left total) equal to the half of Ls (left surround). Or, Rs has a level of -3 dB referred to Ls. Same to Ls in Rt. Lt and Rt are the two encoded stereo channels.
(For acoustic power you have to square the levels!)
Code:
Lt = L + 0.707*C - 0.8165*Ls - 0.5774*Rs
Rt = R + 0.707*C + 0.5774*Ls + 0.8165*Rs
Now it's possible to generate a rear directional steering signal with an operational amplifier, computing Lt+Rt but eliminating L, R, C. The OA output
(Lt+Rt)' = 0.2391*(Rs - Ls)
is fed to a polarity splitter which controls the Ls, Rs output gain.
If amount of Rs < Ls then output will be negative for left directional dominance, and if Rs > Ls the output will be positive for right directional dominance.
So far to the principle of operation, in reality the Pro Logic II decoder is much more complicated.