On May 5 2011, Richard Lee wrote:
This sqrt(2) factor is an endless source of confusion. It seems silly
that W should be divided by sqrt(2) in recoding to restore its value,
which was multiplied by this in the encode to UHJ.
This sqrt(2) factor is WRONG. Where do people come up with such myths?
I think the problem stems from the early material on Ambisonics in that
sometimes the pragmatic engineering decision to use -3dB on W to equalise
average channel levels on a recording of a reverberant environment with a
large number of distributed sources was rolled into the en/decoding
equations and sometimes (in the more "correct", theoretical discussions) it
wasn't. I remember being thoroughly confused by that way back in the days
of my youth...
Dave
The Encoding eqns on http://en.wikipedia.org/wiki/Ambisonic_UHJ_format
are correct and come from Gerzon himself.
"Ambisonics in Multichannel Broadcasting and Video". JAES nov85, 33 (11):
859-871.
The Decoding eqns however, though supposedly coming from the same source,
add an erroneous 1/sqrt(2) factor. They are wrong. If you take this
abomination out, you get ... ___________________________________
Formal UHJ Decode for 3/4 channels.
S = (Left + Right)/2.0
D = (Left - Right)/2.0
W = 0.982*S + j*0.197(0.828*D + 0.768*T)
X = 0.419*S - j(0.828*D + 0.768*T)
Y = 0.796*D - 0.676*T + j*0.187*S
Z = 1.023*Q
___________________________________
.. a formal decode, the Inverse Matrix of the Encoder which recovers WXYZ
exactly. This is what's shown in Gerzon85
Richard, the "signs of j" come out from the mathematics of the complex
Matrix Inversion. The test is that if you encode & decode, you should
recover the original WXYZ (apart from small roundoff errors due to
limited precision of the coefficients)
For 2 channel UHJ, because WXY cannot be recovered exactly, there is a
range of good decodes with different properties.[1]
The one shown on wikipedia is supposedly from Gerzon85 but, because wiki
has added a erroneous 1/sqrt(2) factor, will give very poor results.
Richard, will you reveal the source of your heresy. You are granted
immunity from de-pinnaeing if you talk.
[1] The optimum 2 channel decode is tied in with the design of the
speaker decoder which derives the signals to feed the speakers.
BLaH3 ... "Is my decoder Ambisonic?" Heller et al, AES San Francisco 2008
.... is the definitive reference for design of Classic B-format decoders.
However, 2 channel UHJ decode has other complexities which are yet to be
explained clearly and accurately. Expect a BLaH encyclical on the subject
before the end of the millenium.
In the meantime, let's stamp out incorrect, inaccurate and misleading info.
_______________________________________________
Sursound mailing list
Sursound@music.vt.edu
https://mail.music.vt.edu/mailman/listinfo/sursound
_______________________________________________
Sursound mailing list
Sursound@music.vt.edu
https://mail.music.vt.edu/mailman/listinfo/sursound
