One of the major design goals of the design of the Logic 7 matrix is that the loudness in
any given output of unsteered material presented to the inputs of the decoder should be
constant, regardless of the direction of a steered signal which is present at the same time.
As explained previously, this means that the sum of the squares of the matrix elements
for each output should be one, regardless of the steering direction. As explained before,
this requirement must be relaxed when there is strong steering in the direction of the
output in question. That is, if we are looking at the left front output, the sum of the
squares of the matrix elements must increase by 3dB when the steering goes full left.
We can test the success of our design by plotting the square root of the sum of the squares
of the matrix elements.
See Figure 10 and Figure 11.
Figure 10: The squared sum of lfl and lfr,
using the new design. (For this plot we
deleted the 1/(sin(cs)+cos(cs)) correction
in the rear quadrant, so we could see how
accurately the resulting sum came to
unity.) Note the 3dB peak in the left
direction, and the somewhat lesser peak
as a signal goes from unsteered to 22.5
degrees in the center direction. This
second peak is a result of the deliberate
boost of the left and right outputs during
half-front steering. Note that in the other
quadrants the sum is very close to one, as
was the design intent. The value in the
rear left quadrant is not quite equal to one,
as the method used to produce the
elements is an approximation, but the
match is pretty good.
Figure 11: The square root of the sum of
the squares of lfl and lfr including the
correction to the rear level. Viewed from
the left rear. The unsteered (middle) to
right axis has the value one, the center
vertex has the value .71, the rear vertex
has the value 0.5, and the left vertex has
the value 1.41. Note the peak along the
middle to center axis.
Rear matrix elements during front steering
The rear matrix elements in the ’89 patent are given by:
For the front left quadrant
