Hi,
Date: Sat, 30 Apr 2011 15:34:58 +0100
From: "Richard" <zoanne...@yahoo.co.uk>
I have been a bit of a lurker here for a while, trying to get to
grips with some issues regarding UHJ. Now I know quite a bit about
the decoding of the Quadraphonic matrix systems (I created the
SQ360/QS360 scripts) but am a little confused by the way the decode
formula is written, so I'm hoping someone here can shed some light
on something.
When you encode to UHJ there is a single +90 degree shift used on
both the X & Y signals, with W left untouched:
W' = W*sqrt(2)
S = 0.9396926*W' + 0.1855740*X
D = j(-0.3420201*W' + 0.5098604*X) + 0.6554516*Y
Left = (S + D)/2.0
Right = (S - D)/2.0
So, the question I have is: why is the phase shift required on
decode not -90 degree (where the j should read -j)
W = 0.5*(0.982*L + 0.982*R + j*0.164*L - j*0.164*R)
X = 0.5*(0.419*L + 0.419*R - j*0.828*L + j*0.828*R)
Y = 0.5*(0.763*L - 0.763*R + j*0.385*L + j*0.385*R)
This thread got dropped as far as I can see, but has been nagging at
me, and I've finally got round to wading through the calculations.
The equations match the ones I have found, apart from the
multiplication of W by sqrt(2). The 90 degree phase shift is on W &
X, not X & Y.
It doesn't seem possible to solve the encoding and decoding equations
back to W,X and Y, due to j turning up in all sorts of places.
Gerzon's maths was far in advance of mine, but I suspect that the
numbers may have been arrived at through trial and error.
Working with the numbers given and using W' as W*sqrt(2), I get
(though I may have made the odd error)
W'' = W (1.442) + X( 0.0986) + j*Y(0.1075)
X'' = W( 0.133) +X(0.43) - j*Y(0.543)
Y'' = j* W(0.143) + j*X(0.461) + Y(0.5)
where W'', X'' & Y'' are the B-Format recoding of the the UHJ coding
of the original X,Y,Z This is arrived at by taking j*j= -1, and -*-
as +.
None come back exactly to the original. Notably W'' is pretty near
sqrt(2)* the original. X and Y are about half the original in the
real component and in the imaginary component. Generally unwanted
components are about 10% of their original value
So in X'' the Y component is rotated by -90 degrees relative to its
value in Y'',
In Y'' the X component is rotated by +90 degrees relative to its
value in X'', Which sort of makes sense.
I suggest that W should not be multiplied by sqrt(2) in the encoding.
If so the above equations become
W"" = W (1.019) + X( 0.0986) + j*Y(0.1075)
X"" = W( 0.094) +X(0.43) - j*Y(0.543)
Y"" = j* W(0.101) + j*X(0.461) + Y(0.5)
which looks a bit better, though still not a perfect reconstruction.
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.
I wonder if anyone knows what version of W was used in any encoding
of available UHJ recordings ??
Ciao,
Dave Hunt
_______________________________________________
Sursound mailing list
Sursound@music.vt.edu
https://mail.music.vt.edu/mailman/listinfo/sursound
