Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Martin Leese]

"Richard"  wrote:

> Many thank for that Martin, and although I find the math's a little daunting
> still, it unfortunately brings even more questions  LOL
>
> One is, is it possible to easily implement it using the software a lot of us
> are using?

Sorry, can't help.  I have only ever used
1980s hardware decoders.

> I've read the circuit diagram of the AD-7 UHJ/B decoder, and the
> super-stereo function appears to be quite basic, but I believe, very
> functional, in that
>
> 1, The Super-Stereo control equally varies the level of signal to the X & Y
> phase filters as well as
>
> 2, The pre-set mixing of the W, X & Y signals to match the math formulae as
> described.

The way it works is that the Left, Right input
channels are converted to Sum, Difference.
The stereo width control then varies the gain
of the Difference channel, then Sum,
Difference are converted to W', X', Y' as per
the 1982 equations in Geoffrey's post.
(Obviously it is convenient to combine some
of these steps.)  From this point on, the
design is the same as for a B-Format decoder.

Regards,
Martin
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E-mail: martin.leese  stanfordalumni.org
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Richard]

Many thank for that Martin, and although I find the math's a little daunting 
still, it unfortunately brings even more questions  LOL

One is, is it possible to easily implement it using the software a lot of us 
are using?

I've read the circuit diagram of the AD-7 UHJ/B decoder, and the super-stereo 
function appears to be quite basic, but I believe, very functional, in that 

1, The Super-Stereo control equally varies the level of signal to the X & Y 
phase filters as well as

2, The pre-set mixing of the W, X & Y signals to match the math formulae as 
described.

Has anyone managed to do this in either the software/UHJ response files/Wiggins 
B-Format decoder (and is it still the best out there)

I thought it might be interesting to see if a circuit emulation program could 
be coaxed into creating a software version of the decoder, any ideas?

Sorry for what must be to most some basic questions, and thanks for your 
tolerance of me here.

By the way, if anyone is interested in listening to some Quadraphonic albums 
decoded in a way unthinkable in the 70's (that is with 360 degree seperation) 
please do pop by my blog (oh and there are three UHJ decoded albums I've done 
so far (and phase corrected) - would appreciate some feedback.

http://the-quad-blog.blogspot.com





  Dave Hunt  wrote:

  > Thanks for finding that. I'll have to dig out the papers and see if I
  > can find more info, though I remember being hopelessly confused last
  > time I looked at this, several years back.
  >
  > In the meantime I'll carry on just using the straight UHJ to B-Format
  > equations. These work very well on 'normal' stereo recordings:
  > instant ambisonic surround. How accurate is impossible to say,
  > especially as none of these recordings have ever been 'surround', and
  > the original event is totally inaccessible or even never existed.
  >
  > It seems to work best on recordings made with a crossed pair, or even
  > pan-potted mono. Hardly surprising really.

  Why not use Super Stereo mode?  After all, it
  was intended for "decoding" stereo recordings.
  Geoffrey Barton posted the latest (1985)
  decoding equations for this.

  This information used to be in the
  Ambisonia.com Wiki.  Until the Wiki is
  resurrected somewhere, and rather than
  repeat Geoffrey's post here, I have made it
  available on my Google Site at:
  https://sites.google.com/site/mytemporarydownloads/

  Look under Ambisonic stuff.  As Geoffrey
  points out, Super Stereo uses the same shelf
  filters as B-Format, so that should make things
  easier for you.

  Regards,
  Martin
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  E-mail: martin.leese  stanfordalumni.org
  Web: http://members.tripod.com/martin_leese/
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[Sursound] Question regarding UHJ Encoding - Decoding

[Martin Leese]

Dave Hunt  wrote:

> Thanks for finding that. I'll have to dig out the papers and see if I
> can find more info, though I remember being hopelessly confused last
> time I looked at this, several years back.
>
> In the meantime I'll carry on just using the straight UHJ to B-Format
> equations. These work very well on 'normal' stereo recordings:
> instant ambisonic surround. How accurate is impossible to say,
> especially as none of these recordings have ever been 'surround', and
> the original event is totally inaccessible or even never existed.
>
> It seems to work best on recordings made with a crossed pair, or even
> pan-potted mono. Hardly surprising really.

Why not use Super Stereo mode?  After all, it
was intended for "decoding" stereo recordings.
Geoffrey Barton posted the latest (1985)
decoding equations for this.

This information used to be in the
Ambisonia.com Wiki.  Until the Wiki is
resurrected somewhere, and rather than
repeat Geoffrey's post here, I have made it
available on my Google Site at:
https://sites.google.com/site/mytemporarydownloads/

Look under Ambisonic stuff.  As Geoffrey
points out, Super Stereo uses the same shelf
filters as B-Format, so that should make things
easier for you.

Regards,
Martin
-- 
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E-mail: martin.leese  stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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[Sursound] Question regarding UHJ Encoding - Decoding

[Dave Hunt]

Hi,

Thanks for finding that. I'll have to dig out the papers and see if I  
can find more info, though I remember being hopelessly confused last  
time I looked at this, several years back.


In the meantime I'll carry on just using the straight UHJ to B-Format  
equations. These work very well on 'normal' stereo recordings:  
instant ambisonic surround. How accurate is impossible to say,  
especially as none of these recordings have ever been 'surround', and  
the original event is totally inaccessible or even never existed.


It seems to work best on recordings made with a crossed pair, or even  
pan-potted mono. Hardly surprising really.


Ciao,

Dave


Date: Sat, 7 May 2011 13:54:01 -0600
From: Martin Leese 

Dave Hunt  wrote:


One of these complexities is presumably indicated by the phrase "Note
that two-channel UHJ requires the player to use different shelf
filters than for three- and four-channel UHJ (and B-Format)" at
http://en.wikipedia.org/wiki/Ambisonic_UHJ_format.

Any clues as to why this should be so ?? If we get back something
close to three-channel B-Format, why should it be filtered
differently from  a straight three-channel B-Format ?? The encoding/
decoding has no frequency conscious components. Admittedly, the gains
of the filters may need to differ between 2D and 3D decoding.


See the thread on this mailing list from
December 2008 with the Subject "decoding
an UHJ-B stereo file to Ambisonics Quad".

The thread included this post from Geoffrey
Barton:


Date: Tue Dec 30 12:16:42 EST 2008
Subject: [Sursound] decoding an UHJ-B stereo file to Ambisonics Quad

Sorry to shatter your simple world, but the shelf filters do have to
be different for 2 channel UHJ!

As the BHJ-> 'WXY' decoding has magically produced three channels from
two, there is information missing. This manifests itself as phase-
shifts between the derived WXY signals.

If you optimise the shelves to maximise rv at lf and ev at hf using
these decoded signals, the resulting values are not the same as for b-
format. You also have to watch the way MAG quoted these values as
sometimes he quoted the 'kernel' values for b-format rather than the
'normal' b-format.

Geoffrey



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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Martin Leese]

"Richard"  wrote:

> I didn't think decoding UHJ (as used by Nimbus, Unicorn etc. on their
> releases) required the use of shelf filters, Am I wrong again   LOL

Shelf filters are never "required" (you get to
choose).  They are recommended, particularly
in a domestic setting (small room).

Note that the Nimbus DVD releases have shelf
filtering applied during the decoding from UHJ,
and before the four speaker feeds are burnt
to disc.

Regards,
Martin
-- 
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E-mail: martin.leese  stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Martin Leese]

Dave Hunt  wrote:

> One of these complexities is presumably indicated by the phrase "Note
> that two-channel UHJ requires the player to use different shelf
> filters than for three- and four-channel UHJ (and B-Format)" at
> http://en.wikipedia.org/wiki/Ambisonic_UHJ_format.
>
> Any clues as to why this should be so ?? If we get back something
> close to three-channel B-Format, why should it be filtered
> differently from  a straight three-channel B-Format ?? The encoding/
> decoding has no frequency conscious components. Admittedly, the gains
> of the filters may need to differ between 2D and 3D decoding.

See the thread on this mailing list from
December 2008 with the Subject "decoding
an UHJ-B stereo file to Ambisonics Quad".

The thread included this post from Geoffrey
Barton:


Date: Tue Dec 30 12:16:42 EST 2008
Subject: [Sursound] decoding an UHJ-B stereo file to Ambisonics Quad

Sorry to shatter your simple world, but the shelf filters do have to
be different for 2 channel UHJ!

As the BHJ-> 'WXY' decoding has magically produced three channels from
two, there is information missing. This manifests itself as phase-
shifts between the derived WXY signals.

If you optimise the shelves to maximise rv at lf and ev at hf using
these decoded signals, the resulting values are not the same as for b-
format. You also have to watch the way MAG quoted these values as
sometimes he quoted the 'kernel' values for b-format rather than the
'normal' b-format.

Geoffrey


Regards,
Martin
-- 
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E-mail: martin.leese  stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Richard]

Will do  :-)


   Ignore Wikipedia.  Instead, stick with the
  Gerzon 1985 paper (which yoiu now have).

  Regards,
  Martin
  -- 
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  E-mail: martin.leese  stanfordalumni.org
  Web: http://members.tripod.com/martin_leese/
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Martin Leese]

"Richard"  wrote:

> Phew!!! Firstly, many thanks for the detailed response. I'll admit I find
> the math's related to UHJ & Ambisonics somewhat confusing at times, but 'm
> persevering.

Ignore Wikipedia.  Instead, stick with the
Gerzon 1985 paper (which yoiu now have).

Regards,
Martin
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E-mail: martin.leese  stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[David Worrall]

Given the almost universal acceptance of WP as the font of all information, it 
might be worth someone(s) from this group putting a 'watch for changes on this 
page' tag on the Amb. pages.

drw

On 06/05/2011, at 7:15 AM, Paul Hodges wrote:

> --On 06 May 2011 03:15 + Richard Lee  wrote:
> 
>> The Decoding eqns however, though supposedly coming from the same source,
>> add an erroneous 1/sqrt(2) factor.
> 
> I have corrected these equations on Wikipedia.
> 
> Paul
> 
> -- 
> Paul Hodges
> 
> 
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_
Dr David Worrall
Adjunct Research Fellow, Australian National University
david.worr...@anu.edu.au
Board Member, International Community for Auditory Display
Regional Editor, Organised Sound (CUP) 
Projects Officer, Music Council of Australia 
worrall.avatar.com.au   sonification.com.au
mca.org.au  musicforum.org.au


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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Fons Adriaensen]

On Thu, May 05, 2011 at 06:06:15PM +0100, Richard wrote:
 
>   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)
> 
> ...
>  
>   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.

It is *not possible* to reconstruct the original W,X,Y from just two
signals (L,R). Whatever reconstruction will be a compromise with the
paramters (hopefully) determined by psycho-acoustic considerations.

-- 
FA

 
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Richard]

I didn't think decoding UHJ (as used by Nimbus, Unicorn etc. on their releases) 
required the use of shelf filters, Am I wrong again   LOL


  One of these complexities is presumably indicated by the phrase "Note  
  that two-channel UHJ requires the player to use different shelf  
  filters than for three- and four-channel UHJ (and B-Format)" at  
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Dave Hunt]

Hi,


Date: Fri, 6 May 2011 03:15:51 -
From: Richard Lee 



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.




Snip



[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.


One of these complexities is presumably indicated by the phrase "Note  
that two-channel UHJ requires the player to use different shelf  
filters than for three- and four-channel UHJ (and B-Format)" at  
http://en.wikipedia.org/wiki/Ambisonic_UHJ_format.


Any clues as to why this should be so ?? If we get back something  
close to three-channel B-Format, why should it be filtered  
differently from  a straight three-channel B-Format ?? The encoding/ 
decoding has no frequency conscious components. Admittedly, the gains  
of the filters may need to differ between 2D and 3D decoding.


Ciao,

Dave Hunt
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Geoffrey Barton]

> 
> Message: 14
> Date: 06 May 2011 07:12:21 +0100
> From: dave.mal...@york.ac.uk
> Subject: Re: [Sursound] Question regarding UHJ Encoding - Decoding
> To: Surround Sound discussion group 
> Message-ID: 
> Content-Type: text/plain; format=flowed; charset=ISO-8859-1
> 
> 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...


I think it more likely comes from there being two versions of the equations, 
one encoding from b-format and the other in kernel form. The casual reader 
tends to confuse the direction cosines with the x and y of b-format, MAG 
usually gave both versions in internal documentation as he worked using the 
kernel form himself.

Geoffrey


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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[dave . malham]

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.
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Paul Hodges]

--On 06 May 2011 03:15 + Richard Lee  wrote:


The Decoding eqns however, though supposedly coming from the same source,
add an erroneous 1/sqrt(2) factor.


I have corrected these equations on Wikipedia.

Paul

--
Paul Hodges


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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Richard]

Hi

Thanks for the correction, and I totally agree with stamping out incorrect 
information. I got those figures from a web-site that purported to be the "Bees 
Knees", but unfortunately there's more and more sites with incorrect 
information.

Wikapedea is by far the worst!!!

Your right about there being more to learn about UHJ. I did mention the phase 
issue I found with decoded UHJ material that impairs the front image stability, 
but nobody took me up on it.



  > 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.
  ___
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Richard Lee]

> 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.
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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Richard]

Phew!!! Firstly, many thanks for the detailed response. I'll admit I find the 
math's related to UHJ & Ambisonics somewhat confusing at times, but 'm 
persevering.

Again, thanks

  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



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Re: [Sursound] Question regarding UHJ Encoding - Decoding

[Dave Hunt]

Hi,


Date: Sat, 30 Apr 2011 15:34:58 +0100
From: "Richard" 

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



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[Sursound] Question regarding UHJ Encoding - Decoding

[Richard Lee]

I have questions about UHJ decoding too.

Richard, how did you get your decoding eqns?

My question is about 

http://en.wikipedia.org/wiki/Ambisonic_UHJ_format

It has separate decoding eqns for 2 & 3 channel UHJ.  They are consistent 
except for Y

Y = 0.763*D   + j*0.385*S   2-channel
Y = 0.796*D - 0.676*T + j*0.187*S   3 channel

It's been 30+ yrs since I pretended to unnerstan dis stuff but if IIRC, 3 
channel decoding was supposed to be robust to the T channel. ie if the T 
channel faded out, decode would revert seamlessly to the 2 channel eqns.

The idea was that the Velocity & "Energy" Vector directions would remain the 
same but T would increase the Vector Magnitudes.

I thought I had this scribbled somewhere but all I can find is stuff for 45J 
which is UHJ's immediate predecessor and shows how long ago this was.  I worked 
on the Calrec version of the Transcoder which was UHJ but I can't remember 
doing any UHJ work on the Calrec Ghetto Blasters which was Ken Farrar/Ellis's 
Periphonic System(s).  I did their speaker matrix stuff though.

And where do these eqns come from?  I can't remember a formal 
document/published paper where MAG or Geoffrey Barton state the UHJ Encoding & 
Decoding Eqns.

One coudl take the attitude that only Encoding needs to be specified and the 
user can do what he likes on Decode.  Simple Matrix Inversion would give you a 
formal 3 channel Decode but that doesn't help me cos kunt kont or reed en rite 
.. 8>D

Martin, when we resolve this issue, or even if we don't, we should put 
something in wikipedia stating the source or else something like

"there is no formal source but we have this from Dr. Geoffrey Barton" 
or 
" we got these from reverse engineering the Audio & Design Trancoder & Decoder".

I have been unsuccesful in my application to become a wiki editor cos kunt 

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[Sursound] Question regarding UHJ Encoding - Decoding

[Richard]

Hi all



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)




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