LRL = .71 – .71*G(lr) + .41*.71*G(cs)
LRR = -.71 + .41*.71*G(cs)
For the rear left
LRL = .71*(1 - G(lr)+.41*G(-cs))
LRR = .71*(1 + .41*G(-cs))
(the right half of the plane is identical but switches lrl and lrr.)
The rear matrix elements in the Dolby Pro-Logic are
For the front left quadrant
LRL = .71*(1 – G(lr) + .41*G(cs))
LRR = -.71*( 1 + .41*G(cs))
For the rear left
LRL = .71*(1 - G(lr))
LRR = -.71
(the right half of the plane is identical but switches lrl and lrr.)
A brief digression on the surround level in Dolby Pro-Logic
The Dolby elements are similar to our ’89 elements, but without the boost dependent on
cs in the rear. This difference is in fact quite important. This paper somewhat disguises
the way these decoders are actually used. We derive all the matrix elements with a
relatively arbitrary scaling. In most cases the elements are presented as if they had a
maximum value of 1.41. In fact, for technical reasons the matrix elements are all
eventually scaled so they have a maximum value of less than one. In addition, when the
decoder is finally put to use, the gain of each output to the loudspeaker is adjusted. To
adjust them, a signal which has been encoded from the four major directions – left,
center, right, and surround – with equal sound power is played, and the gain of each
output is adjusted until the sound power is equal in the listening position. In practice this
means that the actual level of the matrix elements is scaled so the four outputs of the
decoder are equal under conditions of full steering.
