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Converting stereo to b-format

2005-09-14

I’ve asked on the Sursound mailing list how to convert a stereo signal to 1st order b-format and received several suggestions. The one implemented for the module posted here yesterday is the super stereo equations given here. Once I’ve finished with the Generator.x and White-out installations I’ll make a more generic patch that can be used to test all of them and wrap as a Pluggo VST so that it can be used by others as well to test the various solutions. Hopefully I’ll eb able to get that working for Mac and Windows.

Below I’ve been winding up the information and suggestions received.

All equations now notated as
M = L + R
S = L – R
j = 90° phase shift
a = Width control varying between 0 and 180°
Dave Malham:
j represents a wide band 90 degree phase difference between channels
- it’s the between channels bit that made it workable in the analog
days. You’d pass both the sum and the difference signals through
similar wideband phase shift circuits one of which was designed to
have 90 degrees of phase shift more than the other. However as Super
Stereo is really a way of using stereo in the context of a UHJ decoder
driven speaker system if you are working with B format exclusively
you may or may not find the extra phasiness inherent in this useful
for you. Your original idea of panning the two channels left and
right into the image works for me and is essentially what Thomas
Chen’s formula does. However this system works best with coincident
pair recordings and if yours are spaced pair the results may be more
variable. as both the sum and the difference signals are highly
frequency dependent ( and before some pounces on that yes so
do coincident pairs but at a much higher frequency…)
Michael’s solution circa late 80’s and used in most Ambisonic
decoders of that period:
W’ = 0.367 M + j 0.3586S
X’ = 0.529 M – j 0.404 S
Y’ = S
WW1977 Stereo
W’ = 0.717 M – 0.291 j S
X’ = 0.717 M + 0.291 j S
Y’ = 0.583 S
Note that you can vary the image width in this scheme by varying
the gain on the difference signal D.
Source: http://www.geocities.com/ambinutter/UHJ_and_Ambisonic_equations.html
Super Stereo:
W’ = 0.65S – 0.27jD(a /180)
X’ = 0.98S + 0.40jD(a /180)
Y’ = 0.75D(a /180)
Source: http://www.geocities.com/ambinutter/UHJ_and_Ambisonic_equations.html
Richard Lee suggests two additional solutions:
W’ = 1.230 M – j 0.499 S
X’ = 1.230 M + j 0.499 S
Y’ = S
Super Stereo:
W’ = 0.8667M – j 0.360 S
X’ = 1.307M – j 0.533 S
Y’ = S
Thomas Chen:
In addition of stereo to B format in my B+ I add L+R to W L-R to Y
and L+R to X. By adjustment of X and Y you are able to get a good
stereo signal with
the B format.

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