[Sursound] any idea's on the background of the stereo equations in the WW1977 article?

[Johan Haspeslagh]

Hello,

I have a question concerning the conversion of a stereo recording to 
ambisonics. In the Wireless World of 1977 articles there are equations for the 
conversion of stereo to W,X,Y equivalent signals. The use of j*Diff term 
doesn't seem to make sense. As I found no background info on them, maybe 
someone in the group has.

The WW1977 article states:
W=0.71*Sum-0.291*j*Diff
X=0.71*Sum+0.291*j*Diff
Y=0.583*Diff
where Sum=L+R and Diff=L-R.

I was puzzled with the addition of the j*Diff, so I tried to find some 
mathematical support for it. The reasoning I did is as follows:

1. As W,X,Y are a representation of a supposed plane wave with amplitude S 
coming from a certain angle phi (phi=0 if straight ahead), we need to suppose 
a analoguous encoding for stereo. I supposed a the sin-like law of encoding 
f.e.:

(L-R)/(L+R)=sin(phi)/sin(30) if loudspeakers are placed at -30 and 30 degrees.

2. As a starting point a naive conversion of the L,R signals (projection of 
L,R on X,Y) to ambisonic-like format gives:
W=Sum
X=Sum*cos(30)
Y=Diff*sin(30)

If we write Sum and Diff in relation to the supposed direction encoding in (1) 
as function of S and phi, then
W=S
X= S*cos(30)
Y= S*sin(phi)

X is independent of the direction, Y correctly encodes the direction neatly. X 
is only correct for the center direction (phi=0) but for all other directions 
the magnitude of the encoded vector is to large (sqrt(X²+Y²)>W).

3. The adding of the j*Diff terms makes af first sight everything even worse, 
it makes the magnitude of X and W  higher and it also introduces a phase 
differences between X,Y and W which is in theory not possible if one encodes a 
plane wave directly.

The only reason I could think of is that by introducing phase differences once 
you construct the loudspeaker signals by adding weighted versions of the W, X 
and Y signal together these phase differences introduce lower amplitudes (than 
adding signals in phase). I did not go through with this calculation yet.

So if someone have some idea's on it, 

Johan





 




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Re: [Sursound] any idea's on the background of the stereo equations in the WW1977 article?

[Robert Greene]

I have not had a chance to look at this in detail,
but one point seems worth noting in advance:
Such a conversion is in the literal sense
impossible. Stereo is a system with two
"degrees of freedom". Horizontal Ambisonics
has three. One can Ambisonics into stereo
(losing information in the process) but not stereo
into Ambisonics.
Roughly speaking one is dealing here with the
fact that Blumlein stereo is symmetric with
respect to front to back. A source centered
in front produces exactly the same result as
the same source in back. Except for polarity reversal.
So one cannot tell if a given source is in front or in
back.
One could assume that in the conversion one
wanted all sources to be treated as if they were
in front.
But intrinsically the whole process is ambiguous--
it can only be done by making some assumptions
about what sort of thing the original thing was.
There is also the isse that a standing wave
with a pressure max/min point , pressure gradient
null at the pickup point would not show up in stereo
but would in Ambisonic pickup.
No way to get that information from the stereo!

Robert

PS I encountered this in making surround out
of the Blumlein stereo for Water Lily's Mahler 5
and Shostakovich 7 recordings. I could generate
(not Ambisonically) some convicing sense of envelopment
(I hope so anyway) but there was no way I could get
the coughs behind in reality (It was recorded in Blumlein live)
not to be folded into the front. They are still there,
sounding as if the coughers in the audience were
in the orchestra. Now if I had had an omni mike feed
at the same spot... then I could have put them where they
belonged. (People complained about this too--they loved
the envelopment I generated but did not love  the coughers in the
orchestra).

On Fri, 20 Jul 2012, Johan Haspeslagh wrote:


Hello,

I have a question concerning the conversion of a stereo recording to
ambisonics. In the Wireless World of 1977 articles there are equations for the
conversion of stereo to W,X,Y equivalent signals. The use of j*Diff term
doesn't seem to make sense. As I found no background info on them, maybe
someone in the group has.

The WW1977 article states:
W=0.71*Sum-0.291*j*Diff
X=0.71*Sum+0.291*j*Diff
Y=0.583*Diff
where Sum=L+R and Diff=L-R.

I was puzzled with the addition of the j*Diff, so I tried to find some
mathematical support for it. The reasoning I did is as follows:

1. As W,X,Y are a representation of a supposed plane wave with amplitude S
coming from a certain angle phi (phi=0 if straight ahead), we need to suppose
a analoguous encoding for stereo. I supposed a the sin-like law of encoding
f.e.:

(L-R)/(L+R)=sin(phi)/sin(30) if loudspeakers are placed at -30 and 30 degrees.

2. As a starting point a naive conversion of the L,R signals (projection of
L,R on X,Y) to ambisonic-like format gives:
W=Sum
X=Sum*cos(30)
Y=Diff*sin(30)

If we write Sum and Diff in relation to the supposed direction encoding in (1)
as function of S and phi, then
W=S
X= S*cos(30)
Y= S*sin(phi)

X is independent of the direction, Y correctly encodes the direction neatly. X
is only correct for the center direction (phi=0) but for all other directions
the magnitude of the encoded vector is to large (sqrt(X?+Y?)>W).

3. The adding of the j*Diff terms makes af first sight everything even worse,
it makes the magnitude of X and W  higher and it also introduces a phase
differences between X,Y and W which is in theory not possible if one encodes a
plane wave directly.

The only reason I could think of is that by introducing phase differences once
you construct the loudspeaker signals by adding weighted versions of the W, X
and Y signal together these phase differences introduce lower amplitudes (than
adding signals in phase). I did not go through with this calculation yet.

So if someone have some idea's on it,

Johan










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Re: [Sursound] any idea's on the background of the stereo equations in the WW1977 article?

[Martin Leese]

Johan Haspeslagh  wrote:
> Hello,
>
> I have a question concerning the conversion of a stereo recording to
> ambisonics. In the Wireless World of 1977 articles there are equations for
> the
> conversion of stereo to W,X,Y equivalent signals. The use of j*Diff term
> doesn't seem to make sense. As I found no background info on them, maybe
> someone in the group has.

I cannot give you any background (and have
never found a derivation).  However, I can give
you a more recent reference.  Visit my Google
Site at:
https://sites.google.com/site/mytemporarydownloads/

and download the file:
Ambisonic_stereo_decoding_equations_1981.pdf

This file came from Geoffrey Barton via Larry
(Lawrence) Gruber.  My thanks to both.

Regards,
Martin
-- 
Martin J Leese
E-mail: martin.leese  stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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Re: [Sursound] any idea's on the background of the stereo equations in the WW1977 article?

[Dave Malham]

Hi,
   The person to really answer this is Geoffrey barton (or perhaps
Peter Craven). I'm sure I have something on this somewhere (possible
in the stuff that went to the FCC??) but I can't find it at present.
I'll have a think about this, but it may have been something to do
with improving on the earlier "Hafler" difference system for
extracting ambience from stereo recordings and placing it on a pair of
rear speakers, which were often set up as an out of phase pair to try
and decorrelate the sound.

Dave

On 20 July 2012 09:55, Johan Haspeslagh  wrote:
> Hello,
>
> I have a question concerning the conversion of a stereo recording to
> ambisonics. In the Wireless World of 1977 articles there are equations for the
> conversion of stereo to W,X,Y equivalent signals. The use of j*Diff term
> doesn't seem to make sense. As I found no background info on them, maybe
> someone in the group has.
>
> The WW1977 article states:
> W=0.71*Sum-0.291*j*Diff
> X=0.71*Sum+0.291*j*Diff
> Y=0.583*Diff
> where Sum=L+R and Diff=L-R.
>
> I was puzzled with the addition of the j*Diff, so I tried to find some
> mathematical support for it. The reasoning I did is as follows:
>
> 1. As W,X,Y are a representation of a supposed plane wave with amplitude S
> coming from a certain angle phi (phi=0 if straight ahead), we need to suppose
> a analoguous encoding for stereo. I supposed a the sin-like law of encoding
> f.e.:
>
> (L-R)/(L+R)=sin(phi)/sin(30) if loudspeakers are placed at -30 and 30 degrees.
>
> 2. As a starting point a naive conversion of the L,R signals (projection of
> L,R on X,Y) to ambisonic-like format gives:
> W=Sum
> X=Sum*cos(30)
> Y=Diff*sin(30)
>
> If we write Sum and Diff in relation to the supposed direction encoding in (1)
> as function of S and phi, then
> W=S
> X= S*cos(30)
> Y= S*sin(phi)
>
> X is independent of the direction, Y correctly encodes the direction neatly. X
> is only correct for the center direction (phi=0) but for all other directions
> the magnitude of the encoded vector is to large (sqrt(X²+Y²)>W).
>
> 3. The adding of the j*Diff terms makes af first sight everything even worse,
> it makes the magnitude of X and W  higher and it also introduces a phase
> differences between X,Y and W which is in theory not possible if one encodes a
> plane wave directly.
>
> The only reason I could think of is that by introducing phase differences once
> you construct the loudspeaker signals by adding weighted versions of the W, X
> and Y signal together these phase differences introduce lower amplitudes (than
> adding signals in phase). I did not go through with this calculation yet.
>
> So if someone have some idea's on it,
>
> Johan
>
>
>
>
>
>
>
>
>
>
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-- 

These are my own views and may or may not be shared by my employer

Dave Malham
Music Research Centre
Department of Music
The University of York
Heslington
York YO10 5DD
UK
Phone 01904 322448
Fax 01904 322450
'Ambisonics - Component Imaging for Audio'
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Re: [Sursound] any idea's on the background of the stereo equations in the WW1977 article?

[Eero Aro]

Johan Haspeslagh wrote:

In the Wireless World of 1977 articles there are equations for the

...

where Sum=L+R and Diff=L-R.


I know nothing about the mathematics, and possiby this has nothing
to do with your problem, but I want to make a note about the decoder
construction, as I did build the WW decoder in the distant past. I had
difficulties in getting the gadget working and almost threw it away and
thought the whole thing was just crap.

This was because there isn't a schematic in the article for the LR/MS
matrix at all. As a sound engineer I had been taught that
M = L + R and
S = L - R
...and built the LR/MS matrix according to that.

The result of the decoding was a total mess and all directions were
completely wrong. I got it right only after I understood that the
S signal was actually made by inverting the L signal, not the R, and
summing the signals together.

The LR/MS matrix is made in the same way in the Elektor, Integrex and
Minim decoders:
M = L + R
S = - (L - R)

I guess this is just a practical solution and saves some components.

Eero
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Re: [Sursound] any idea's on the background of the stereo equations in the WW1977 article?

[Eero Aro]

Hi All

For those who don't know the Wireless World decoder articles,
they are in Sampo's Motherlode:

http://decoy.iki.fi/dsound/ambisonic/motherlode/source/Surround%20Sound%20Decoders%20Pts%20567%20WW%201977.pdf

There is also a list of corrected component values at the end of the pdf.

Eero
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