> 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? 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
