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Help for DIY Enthusiasts

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I am occasionally asked by DIY enthusiasts to assist with the design of their own Ambisonic decoders. Here are two e-mail messages and a PDF file which encapsulate my knowledge (and also my ignorance) in this area. Be aware that the W, X and Y channel gains are those inside an Ambisonic decoder and the sqrt(2) boost, applied to X and Y to equalise the energy in the channels, has been removed.


Shelf Filters

Subject: Re: LEVEL!!! mode select
Date: Sun Oct 4 21:33:35 1998
From: Martin J Leese

There is good news and bad news.

The bad news is that the paper distributed does not seem to 
contain an explanation of how to derive the appropriate shelf filter 
gains for different speaker layouts, etc.  The good news is it does 
contain enough information to reconcile the apparently different shelf 
filter gains in the various papers for horizontal four-speaker UHJ and 
B-Format.

For 2-channel UHJ decoding the high-frequency gains are 1.0.  Some
papers suggest that the low-frequency gains for UHJ should be 1.0, but 
this turns out to be only because the suggested circuit for switchable 
gains holds the low-frequency gain at 1.0 and so pushes the required 
low-frequency gains into a prior resistor matrix.  Other minor 
differences are explained by the shelf filter gains for UHJ differing 
slightly from its predecessor System 45J.

Here are the shelf filter gains.  I stress that these are for a 
horizontal four-speaker layout only.

                    Low    High

    B-Format: W    1.00   1.2247
              X,Y  1.00   0.8660

    UHJ:      W    0.646  1.00
              X,Y  1.263  1.00
              B    0.775  1.00

In truth, there is still some disagreement between the papers about
the gains for the B-channel of UHJ (used for Forward Preference).  I 
have shown above the gains from the Gerzon 1985 reference and suggest
you use its matching formulae.  

The Gerzon 1977d reference states that the gains for Super Stereo are 
very similar to B-Format.  What is still a mystery, at least to me, is 
what gains are appropriate for five and six speaker layouts.  (The 
gains for B-Format periphony are in Gerzon 1980.)  What is also 
missing is the decoding equation for Super Stereo.  There is one in 
Gerzon 1977d, but it states it is a compromise (also, I don't trust 
this reference).

I list below the various papers that now seem to have been 
reconciled.

Regards,
Martin
______________________________________________________________________

Michael A. Gerzon, "Design of Ambisonic Decoders for Multispeaker
Surround Sound", 1977a.  [This is the paper distributed.]

* M.A. Gerzon, "The Optimum Choice of Surround-Sound Encoding 
Specification", Preprint no. 1199 of the 56th Audio Engineering 
Society Convention, Paris, (1977b Mar. 1)  
(About optimising 2-channel encoding for surround-sound - the theory 
behind UHJ.  Very mathematical.)

Michael Gerzon, "Multi-System Ambisonic Decoder",
  Part 1: "Basic Design Philosophy", Wireless World, vol. 83 no. 1499, 
    pp. 43-47 (1977c July)
  Part 2: "Main Decoder Circuits", Wireless World, vol. 83 no. 1500, 
    pp. 69-73 (1977d Aug.)
  Later parts never written & published.

* M.A. Gerzon, "Practical Periphony", Preprint 1571 of the 65th Audio
Engineering Society Convention, London (1980 Feb.)  
(A relatively non-technical account of practical with-height 
full-sphere Ambisonic decoding.)

*** M.A. Gerzon, "Ambisonics in Multichannel Broadcasting and Video", 
J. Audio Eng. Soc., vol. 33 no. 11, pp. 859-871 (1985 Nov.)  
(Possibly the best overview of classic Ambisonics.) 

To be clear, use the B-Format shelf filter gains for Super Stereo.

The transition frequency at which the shelf filter gains change from the low- to the high-frequency values is a design compromise. Theory suggests it should be set to 700 Hz so that the distance between your ears is half a wavelength. However, in most Ambisonic decoder designs it is lowered to 400 Hz. This increases the effective listening area, but at the cost of poorer localisation at the sweet spot.


Subject: Decoder equations
Date: Sun Aug 15 20:49:42 1999
From: Martin J Leese

Hi Folks,

I am no longer sure who is part of this informal group designing the
home build Ambisonic decoder.  If I have missed anybody out, please 
forward this message to them.  My chosen role in the group has been 
simply to feed you references and design equations.  As some of you 
may know, I am shortly moving to California to become a full-time 
graduate student at Stanford University.  

This means that my library of Ambisonic papers and my hi-fi are going
into storage for several years.  Also, I do not know how much free 
time I will have to devote to stuff like Ambisonics.

To date, you have (quite correctly) only concerned yourselves with the
wide-band 90-degree phase shifters.  However, before disappearing I 
thought I had better feed you design equations for other parts of the 
decoder.

I have already fed you what information I have on shelf filters.  If
you would like me to recirculate this then let me know in the next few 
days.  Other parts of the decoder are:

Speaker Distance Compensation

This compensates for the non-planar wavefronts emitted by point 
speakers placed at a finite distance from the listener.  A simple 
high-pass R-C filter is used with a -3 dB point at a frequency of 
(53/r) Hz, where r is the distance in metres from the speakers to a 
central listener.  Only the X and Y signals are filtered, not W.  Note 
that it is the *phase* behaviour of the simple R-C filter that is 
important; the fact that it also filters out stuff below 20 Hz or so 
is irrelevant.

Forward Preference

This is used only with UHJ decoding, not B-Format or Super Stereo.  
It pushes phasiness to the rear of the sound field where it is less 
offensive.  With no forward preference (a = 0), the phasiness is 
distributed equally around 360 degrees.  The transformation is:

    new W = W
    new X = X
    new Y = Y - a.(jW)
    where a = a constant
          j = 90-degree phase shift

Now, what value of "a" to use?  In theory, 0 < a < 1.  Gerzon's patent
4081606 suggests 0.333 < a < 0.5.  Gerzon 1977 (refs at end) uses 
a = 0.3.  Gerzon 1985 suggests 0 < k' < 0.7 which is equivalent to
0 < a < 0.49.  I would either allow 0 < a < 1.0 and experiment or go
with the most recent reference, Gerzon 1985.

Forward Dominance

This is a "zoom control" that moves the listener forwards or backwards 
in the sound field.  If the listener is moved forward then sounds at 
the front get louder and sounds at the back get softer.  Note that 
this cannot be accomplished by simply adjusting the volumes of the 
front and rear speakers because all speakers cooperate to place sounds 
at the front (or anywhere else).  The amount of forward dominance is 
expressed in terms of the total dB gain at the front relative to the 
rear.  The transformation is:

    new W = a.W + b.X
    new X = a.X + 2.b.W
    new Y = Y
    where a and b are constants related by:
        a = 0.5(L + (1/L))
        b = (1/(2.sqrt(2))).(L - (1/L))
        L*L = (1 + u)/(1 - u)
        u = 0.1(Gain in dB)

(Obviously, this "a" is different from the one used for Forward 
Preference.)  Note that when a = 1 and b = 0 (given by L = 1), the 
transformation does nothing.  

Some examples of suitable values of "a" and "b" are given below.  
I have listed the square of L just to simplify the values in that 
column; you don't actually need these.  Note that the same values 
occur more than once in the table, thus simplifying the necessary 
circuit (he said, confidently) :-)

    Gain (dB)    u      L*L    a        b
       +6       0.6     4     1.25     0.5303
       +3.333   0.3333  2     1.0607   0.25
        0       0       1     1.0      0.0
       -3.333  -0.3333  0.5   1.0607  -0.25
       -6      -0.6     0.25  1.25    -0.5303


Well, that's all folks.  Best of luck.

Regards,
Martin
______________________________________________________________________

Michael Gerzon, "Multi-System Ambisonic Decoder",
  Part 1: "Basic Design Philosophy", Wireless World, vol. 83 no. 1499, 
    pp. 43-47 (1977 July)
  Part 2: "Main Decoder Circuits", Wireless World, vol. 83 no. 1500, 
    pp. 69-73 (1977 Aug.)
  Later parts never written & published.

*** M.A. Gerzon, "Ambisonics in Multichannel Broadcasting and Video", 
J. Audio Eng. Soc., vol. 33 no. 11, pp. 859-871 (1985 Nov.) 
(Possibly the best overview of classic Ambisonics.) 

Super Stereo

Here is a 1981 reference for the "decoding" equations for stereo sources:


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