Multichannel Stereo Matrix Systems: An Overview JOHN M. EARGLE Mercury Record Productions, New York, N.Y.
In increasing profusion, "4-2--4" matrix playback systems are being introduced to an already confused market place. All of these systems fall short of the "four-channel" performance claimed for them, but many of them are suprisingly accurate in their recreation of auditory perspective around the compass. This paper will examine the basic properties of 4-2--4 matrices along with some of the embellishments which have been used to improve their performance. Finally, higher order matrix systems will be examined briefly.
INTRODUCTION: The last two years have seen considerable attention given to various 4-2--4 matrix systems, which take four inputs, encode them down to two normai stereo channels, and then on playback decode the two transmission channels back to a four-speaker array, The technique is very straightforward, and the very terms "encode" and "decode" make it sound more cornplicated than it really is. Basically, a two-channel matrix array takes a pair of stereo channels and reconciles their performance to the demands of reproducing sounds in a 360 째 arc around the listener. There is no reason why the playback array should have four loudspeakers; three, five, even six or more would do just as well. The choice of four seems to have been arrived at mainly as a commercial alternative to the discrete four-channel tape playback systems which have been introduced in the last year and a half. Some years ago, Klipsch [12] proposed a bridged center loudspeaker located between a widely spaced ster-
simply embellishments of this approach. In recent years, Scheiber [15] introduced the notion of "around-thecompass" localization by means of a four-loudspeaker array in a two-channel matrix, and to this basic array he added a powerful concept, playback signal expansion. This provided an enhancement of separation between the four reproduced signals by emphasizing the differences between them; a channel not in demand would have its gain reduced while one in demand might have its gain increased, the "gain riding" being tailored in such a way that the listener was unaware of the manipulation. The gain riding concept is an important part of some 4-2-4 systems, but a detailed discussion of it is not necessary to a thorough understanding of matrix systems in general. In this paper we will deal primarily with the basic properties of linear matrices themselves in transmittingdirectionalinformationaround the compass.
eo pair as a means of solidifying the normal phantom center produced by in-phase components in the stereo recording. In a way, he was using three quarters of one of today's four-channel matrix arrays. The bridged center speaker was fed a sum signal (left plus right). With the addition of a difference signal (left minus right or right minus left) fed to a rear speaker, the matrix would have been completed, and today's matrix systems are
4-2-4
552
BASIC TWO-CHANNEL
MATRIX
PROPERTIES
Systems
Fig. 1 illustrates a method for determining coefficients for encoding any number of inputs into two transmission channels and recovering them on playback. As shown, the resignated points along the O-axis are for the Scheiber and Dynaquad four-speaker arrays. Their respective inputs (ABCD) to the two transmission chanJOURNAL OFTHEAUDIOENGINEERING SOCIETY
Cos O
Sin
Recovering
8
_¢">
the four inputs,
A' = 0.707(Lt)
-- 0.707(R 0 = A + 0.707B -- 0.707D
C' = 0.707(Lt) + 0.707(Rt) ----C+ 0.707B + 0.707D D' ----0.0(L0 + 1.0(Rt) = D -- 0.707A + 0.707C. '/_ -_° ',I i
_
'
'r e _°
_ ',I , t
/I '
i
I
B_ck
,, , Cen[er , I L
Le!
, I ,
,
I
I
B
, ', A
C
, I C Fig. 1. Determination
I
, _ R_ght , J , I
, _ t,
,' , (Back)
I
D
The corresponding loudspeaker positions for this matrix B' =shown 1.0(Lt) + O.O(R are as circles in t) Fig.= 2.B + 0.707A + 0.707C Note that in laying out these two examplesof 4-2-4 matrices the four inputs were assigned equally spaced positions along a 180 ° range covered by the 0-axis. q_e resultingsine and cosine coefficientsguaranteethat the acoustical power radiated in the two-channel mode will be equal for the four input signals and that the amplitude levels in the four-speaker array will be equal. In both cases this is due to the simple trigonometricidentity, sin 20+cos 20= 1.
Scheiber
, ! D
of coefficients for 4-2-4
^r=,v
Both 4-2--4 matrices described may be termed balanced, since the encoding is done at equal intervals along Dynaquac' Ar_,v the O-axis, and the decoding is done at those same encoding,
points
along
nels have their coefficientsdetermined by the values of
cos_
the cosine function for the left transmission channel and the sine function for the right channel. For the Scheiber array this corresponds to
_/---_/j-_"_
R t = --0.383A
+0.383B+O.924C+O.924D.
L t and Ri are the signals ing the two encoded coding coefficients: A' = B' = nels, C' = D' =
0.924(LO--O.383(Rt) 0.924(Lt) + 0.383(Rt) and we decode each of 0.383(Lt) + 0.924(Rt) --0.383(Lt) +0.924(Rt)
that
axis.
While
the
two-channel
per-
s_ e
(1)
in the two transmission
channels
(4)
cban-
by the corresponding
,
_
....
,
....
_--_ o
en-
= A +0.707B--0.707D = B + 0.707C + 0.707A the four inputs by multiply= C + 0.707B + 0.707D = D+O.707C--O.707A.
//-ti(t°
:
_°
, _:'ii_ _
*B°
_'__i
a_
(2) Each of the inputs has been recovered at unity level along with its adjacent neighbors down 3 dB and the
Fig. 3. Determination of coefficients for 3-2-3 encoding.
diagonal signal absent. The corresponding speaker array for the Scheiber matrix is shown by the squares in Fig. 2. Similarly, the encoded form for the Dynaquad matrix
formance of these matrices is different, the performance over the four-speaker array is the same; each signal appears at its two adjacent speakers down 3 dB and is absent from the diagonal speaker.Referringto Fig. 1, the difference between the two matrices is determined by the incremental angle a0. Note that a displacement of A0 corresponds to a shift in the loudspeaker array of 2A0. This is the result of having to represent the 360 ° of
is L t = 0.707A + B + 0.707C + 0.0 D R t -= --0.707A + O.OB+O.707C+D.
_
(_)
(_ _ ......
(3)
r-----]
arc, point by point, in the playback array by a 180° portion of the O-axis. Any value of a0 may be used and, providing that encoding and decoding take place at equally spaced points along the 180 ° section of the 0axis, the final four-speaker array will have the same
(_
4-2-4 separationcharacteristicswe have given. 3-2-3 Systems There is no reason why the two-channel matrix array should use four loudspeakers. What about three, for
f-----t
_
{o I
Fig. 2. Speaker locations for 4-2--4 matrix systems, JULY/AUGUST1971,VOLUME19, NUMBER7
example?A pair of 3-2-3 matrix arrays is shown in Fig. 3, and their corresponding loudspeaker arrays are shown in Fig. 4. Here obviously the crosstalk between 553
JOHN M. EARGLE but it would certainly interfere with the localization
of a
sound image assignedto a center rear position. In the Dynaquad array the same condition must exist, but here, ._'"_]' ·
L_J
_
owing
[__2_1
phase conditionwill existeither betweenthe rear and left speakers or the rear and right speakers. As shown here, the condition exists between the rear and right speakers.
(_
one loudspeaker and its two neighbors is 6 dB. Outside of the drastic rearrangement of furniture that the 3-2-3 playback matrix often calls for, it is generally desirable, The 6-dB adjacent-channel separation it provides yields far less ambiguity than the 3-dB separation characteristic of the 4-2--4 arrays, and for purposes of conveying an impression of classical "direct-ambient" recording it is indeed satisfying. The encoding and decoding equations for both these solutions are given below. The first is for the speakers arrayed left, right, and front, an arrangement similar to Cooper's "triphonic" system [4]:
and
symmetry
of
the
speaker
array,
the
out-of-
shift to the playback These tend to distributenetworks phase relations between array. the four loudspeakers in
Fig. 4. Speaker locations for 3-2-3 matrix systems,
Lt = 0.707A-
the
135 ° instead of --45 ° would move this condition to the (The use of the alternativerear encodingcoefficientsat otherpair.) There are a number of ways of getting around this problem, the simplest being the addition of all-pass phase-
_i_....
(_)
to
0.258B + 0.965C
Rt = 0.707A + 0.965B -- 0.258C
(5)
exists between such a way that speakers no completelyout-of-phasecondition when phantom images are panned between them. An example of this technique is shown in Fig. Sa. Here the rear-speaker out-of-phase condition has been changed to 90 °, and a 45 ° difference exists between the side pairs. The front pair has not been altered, thus guaranteeing proper and unambiguous localization of a front center image. Fig. 5b shown another approach in which the rear pair is in phase while each side pair is 90 ° out of phase. In this case, all-pass phase-shift networks have been used to cause a signal assigned to the rear center to appear in phase between the rear pair, and as a consequence of this, signals intended as phantom images between the side pairs will be 90 ° out of phase, leading and lagging as indicated. Similar problems exist with the two examples of 3-2-3 matrices which have been discussed, but the wider spacing of loudspeakers and the 6-dB crosstalk factor probably tend to minimize localization ambiguities. A similar
A' = 0.707(Lt) -- 0.707(Rt) = A + 0.5B + 0.5C B' = --0.258(Lt) + 0.965(Rt) = B + 0.5A -- 0.5C C'=The0.965(Lt)--O.258(Rt) = C +0.SA--0.5B. obvious speaker arrangement for this matrix(6)is
J_
B
matrix has its speakers indicated by squares in Fig. 4, and the corresponding encoding and decoding equations are L t = --0.707A q- 0.258B + 0.965C shownby the circlesin Fig. 4. The mirror image of this R t = 0.707A + 0.965B + 0.258C (7)
A' = --0.707(Lt) + 0.707(Rt) = A Jr 0.5B -- 0.5C and B' = 0.258(L 0 + 0.965(Rt) = B + 0.SA + 0.5C C' = 0.965(Lt)+O.258(Rt) = C--0.5A +0.5B.
(_
[_
-C2_1
__
(8)
This last matrix closely resembles a normal twodifferentially connected loudspeaker placed behind the listener, an arrangement which has been gaining in popularity because of the enhancement it often gives standard recordings which contain a good amount of randomly correlated information, such as reverberation. channelstereoarrayto whichhas beenaddeda simple
Ambiguities in Matrices It is noticed in the Scheiber array (Fig. 2, Eq. (2)) that the signals' in the rear pair of the four-speaker array contain out-of-phase terms. Since this condition exists behind the listener it is not necessarily disturbing to him, 554
I_
/
j_
(1') I
_ _[_-1 'L2J Fig. 5. Two methods for correcting localization ambiguities in 4-2--4 matrices, r JOURNAL OFTHEAUDIOENGINEERING SOCIETY
MULTICHANNELSTEREOMATRIX SYSTEMS:AN OVERVIEW L _
this correspondsto in-phasesignalsin the rear pair with coefficientsof 0.7. If such a four-channelrecordingis fed
L g
Xxx,,x
2,<o
<
_ :+R /
_
_..._.
L_ = 0.924 (0.707 rear) --0.383 (0.707 rear) = c
a
a
b _ '_^
6_
/.-:
--_
--_,._ ..,rB
--'_ d
Fig. 6.array, Vectorb. representation different arrays, Dynaquad Basic Scheiber for array, c. 3-2-3 arraya. with front center, d. 3-2-3 array with rear center. use of all-pass phase-shift networks would not be as generally useful here as with the 4-2-4 matrices, Vector
Representation
of Two-Channel
RE = 0.383rear --0.383 (0.707 rear) + 0.924 (0.707 rear) _0.383 rear (9) and
-
e
have to the thebasic following Scheiber4-2-4 result: encodingmatrix, then we
Matrices
In any two-channel transmission system we can represent the instantaneous value of both input signals on the x-y plane. The orthogonality of the two axes represents the mutual exclusivity of the two systems, and the cross section of a stereo disk groove illustrates this directly since its two mechanical inputs are 90 째 apart in space. Fig. 6 shows several combinations of individual and paired inputs to a two-channel system. In Fig. 6a we see the stylus contours for individual left and right inputs as well as L = R (lateral) and L ------ R (vertical) modes. These four vectors represent the inputs to the Dynaquad matrix, while those of Fig. 6b represent Scheiber system inputs. The 22.5 째 difference in orientation is obvious, as is the fact that the projection of any unit vector on its neighbor is 0.707 (3 dB down). Just as clearly, Fig. 6c and d illustrates the projection of a vector on its neighbor as 0.5 (6 dB down), and this represents the two examples of 3-2-3 matrices discussed tfitionsare extremelyuseful for constructionand analysis, and this extends even to three-channel matrix arrays aswewillseelater. Interfacing 4-2-4 Matrices with Discrete Four-Channel Systems matrix arrays, vector represenearlier. For two-channel
B' = 0.924(Lt) + 0.383(R 0 = 0.50 (rear) C' -- 0.383(Lt) + 0.924(Rt) = 0.50 (rear) D' = --0.383(L 0 + 0.924(Rt) = 0.21 (rear).
(10)
Since B' and C' are respectively, the front-left and front-right speakers --O'383(Rt) of the 4-2-4 = playback A' = O'924(LO O'21(rear) array, it is clear that the signal intended for rear localization will be localized front center, because it is 7.6 dB louder in the front pair than it is in the rear pair, In fact, in the Scheiber array there is an error in localizing encoded signals panned anywhere between the rear pair of a discrete four-channel array, but the error can be ignored in most cases. Only where there is the intent of panning a signal around the compass is there trouble in the rear quadrant. There are a number of solutions to the general problem of relating panned signals in a discrete four-channel array to a 4-2-4 array, and they usually employ aU-pass phase-shift networks in both encoding and decoding. Earlier we discussed the role of these networks in reducing ambiguities in the playback array. Now we will see how they can be used to reduce ambiguities in encoding. The Sansui Company of Japan has proposed, in a recent specification sheet for their consumer matrix playback unit, an encoding-decoding method which eliminates these ambiguities [14]. Their encoding matrix is shown in Fig. 7a. Note that a signal intended for rear center in a four-channel array will be fed to the A and D inputs of the matrix and will end up in the encoded two channels out of phase, the encoded condition representing rear-center localization. The eota
B c째----
.q24
C-sc, .383
o _,
B
.92a ^_ .383D
!:E_
._ D.._^ '9_4B* '_83c
'i_
_'
A given input can be assigned a unique direction in a 4-2--4 matrix array by determining the .appropriate voltage ratios and polaritiesin the two transmissionchanavailable at the point of 4-2-4 ofencoding. a fournels. However, a multitude inputs isUsually not 'normally track intermaster has been prepared, and it is this tape
Decode.924 L tt _-' Rt_ C[rOd_i'924L D_M Matrix _'383 R t ,383 L_0-----_
"CA' OB'
product as well as the 4-2-4 matrix product. Here there can be problemsin relatingthe directional aspectsof discretefour-channelrecordingwith the which is to the be the progenitor of the discrete four-channel corresponding matrix playback. For. example, assume that a signal is to be assigned to a phanto m 'position behindthe listener.In the discrete four-channelarray _JULY/AUGUST 1971,VOLUME .19,NUMBER 7
L- .9__ ' OD' L_+ .92_at OC' b _ Fig. 7. a. Sansuiencoding matrix, b. Sansui decoding.matrix. R_o----i _.383
555
JOHN M. EARGLE a Aoe o__ o__[_,c__ c o_
being reproduced 7.6 dB lower than the front pair B and L
4o
^'. Bc
__
___
Dynaquad array, but if the input to A ismaterial reverberant, as encoding discrete four-channel program into the in the case of a classical recording, then the absence of A in the monophonic code would not necessarily be a
_o , ' I *--_+-
.........
__
Scheiberhas altered his basic encoding--decoding arrays in such a way that monophonic compatibility is
__
b
c ______
D ii ^ Fig. 8. a. Scheiber method of ensuring monophonic cornpatibility, b. Vector representation before phase shift, e. Vector representationafter phaseshift, responding playback matrix is shown in Fig. 7b. The outof-phase A and D signals are now converted to an in-phase condition by the all-pass networks, while a -490 ° phase difference will be observed between the right pair and left pair of loudspeakers, respectively, It would appear then that we must use all-pass phaseshift networks in both encoding and decoding in order to avoid ambiguities in 4-2-4 matrices when interfacing them with discrete four-channel recordings. We must also accept what effects, if any, these networks may have on the quality of the program, Two-Channel
Performance
of 4-2-4 Matrices
Perhaps the most important claim of proposed 4-2-4 matrix systems is their promise of normal stereo compatibility, and to a great extent they seem to meet this requirement. Where the encoding has been done via the rules previously stated, it is guaranteed that the acousticai energy levels of the inputs will all be equal in the two-speaker array, and all that remains is a consideration er how these signals will be localized in the two-channel format. When signals are in phase between the two playback speakers, they will be clearly localized along a continuum between those speakers, depending on their relative levels. Where out of phase conditions exist, the effect is not usually noticed as such, unless the two out of phase signals are of equal amplitude and the listener is evenly located between the two loudspeakers. In this case, the listener is aware of a bizarre and vague sensation; the sound seems to be coming from a number of directions at once, and uncomfortably so, but this situation occurs only when there has been a specific input which shows up equally and out of phase in the two channels and when the listener is on the axis of symmetry between the two loudspeakers. For the most part, the various 4-24 matrix systems can be considered compatible for two-channel playback. Monophonic
Performance
of 4-2-4
Matrices
Here we begin to encounter problems with many of the proposed matrices. When there have been no special measures taken to ensure monophonic compatibility, the mono signal array, defined as L t + Rt, may result in significant differences in the reproduced levels of the four inputs. Considering the basic Scheiber array (Eq. (1)), Lt 4- R t, results in the two rear inputs A and D 556
sults in input signal C being 3 dB higher than B and D, while A isDynaquad totally absent. is a severe criticism reof C. In the array, This monophonic reproduction
guaranteed. At the outputof his decoderhe has added all-pass 45 ° phase shift networks, and these ensure equal badthing. amplitudes of the four inputs in the monophonic mode. At the input to his decoder, these phase shifts are canceled, and decoding takes place as usual. The scheme is shown in Fig. 8a, and the corresponding vector diagrams for the four inputs are shown in Fig. 8b. The A and D vectors in Fig. 8b project on the Lt 4R t axis at _alevel substantially lower than the B and ¢ vectors. However, after the 90 ° all-pass phase shift between Lt and R t has been added, the vectors take on the elliptical contours shown in Fig. 8c, and all four unit inputs project on the lateral axis at a value of 0.7. The same approach could be used with the Dynaquad array, and the resulting change in the vector representation would be as shown in Fig. 9. Here again, all unit inputs project on the lateral axis at a value of 0.7, and the effect of the phase shift on the A and C vectors is to make their contours circular, or helical, if they are viewed along the time axis. There is no effect on the B and D vectors since these exist exclusively in the left and right transmission channels, respectively. As we have seen, all-pass phase-shift networks can be employed in 4-2-4 matrix systems for a variety of purposes: to correct for encoding ambiguities, Iocalization ambiguities in the four-speaker playback array, and monophonic imbalances. To a great degree these problems are interrelated, and they can be combined in an endless variety of ways in puffing together 4-2--4 matrix systems. Separation
Enhancement
(Gain
Riding)
With a 3-dB adjacent-speaker crosstalk factor, 4-2--4 matrices call for some kind of "enhancement" if their performance is to rival that of discrete four-channel systems. So far this enhancement has taken the form of signal expansion in the playback mode, and the desire to do this well for all kinds of program input is likely to remain an open-ended engineering challenge for years to come. Scheiber ha s approached the problem in a detailed A B _(
%
/
/
%
/ %
>C
^ c ....
,_
__!.i _._
o
a b Fig. 9. Monphonic compatibility with Dynaquad array, a. Vector representation before phase shift, b. Vector representation after phaseshfft. JOURNAL OF THE AUDIO ENGINEERING SOCIETY
MULTICHANNEL
Lt 0
xS_
A'
B.
STEREO MATRIX SYSTEMS: AN OVERVIEW
Voicematrix. The Electro-Voice matrix works very well in normal two-channel playback. The two front signals appear
_
Gain
c..... _ Fig. 10. Basic elements of balanced 4-2-4 gain-riding ehhancement scheme,
slightlypanned in betweenthe speakers,and the two rear signals, under normal stereo listening conditions, will be gain riding the present form of Under the Electroheard pannedemployed in closerin toward the middle. more stringent monitoring conditions these signals may appear outside the loudspeaker array. In mono, the two rear signals are about 8 dB below the front pair, and this requires a very careful consideration of musical input values. If the rear signals are primarily reverberant, then their attenuation in mono may be tolerable, and even
way, the bare essentials of which are shown in Fig. 10. In the playback matrix, a diagonal pair is fed to a complex logic function whose two outputs control the gain of diagonal pairs in the four-speaker array. The gain-control function is continuously variable, and it works in such a way that, when a signal is present in one of the inputs to the encoding matrix, say, A, then the playback gain control governing B t and D' is zero. As we have seen earlier, A t and Ct are mutually exclusive; so in the gain-controlled playback array, input signal A will appear only at the output speaker A t. Accordingly, the other three input signals can enjoy the same exclusivity when they alone are called for, and because of the total separation which exists diagonally in the 4-2--4 array, only two gain-control voltages are necessary. In between, of course, the complementary diagonal gain functions
desirable irt some cases. In pop recording where the aim is to have primary information over all four speakers, considerations of mono compatibility would likely lead to the assignment of important melodic and rhythmic lines up front, while the rear pair would carry lines more intended for embellishment. It turns out that in practice many requirements can be worked out by very careful 4-2-1 monitoring. After all, there are at least two defini-
are riding in and out as need be. When all four inputs are going at full tilt, the gain control operation is effectively defeated. Its maximum operation takes place at times when a single input is emphasized over the remainina three, The niceties of 4-2-4 matrix gain riding are very much the same as for gain riding in more familiar context. The aim is simply that the gain manipulations are not observed as such by the listener, insofar as this is possible, and this demands a careful determination of attack and release times as well as threshold controls,
Historically the recording industry has progressed by powers of two in order; the capability of master recording has gone from one-, to two-, four-, eight-, and finally 16-track recording. The consumer playback formats have likewise held to a 1-2--4 progression.Suppose that the industry had elected to promote threechannel playback systems. Then the problems of devising a four-speaker matrix would have been far simpler. A 4-3-4 matrix can be visualized graphically by simple extension of the two-dimensional vector array shown earlier.
VARIATIONS
As shown in Fig. 11, the three channels can be represented by three mutually perpendicular unit vectors in
IN BASIC
4-2-4
MATRIX
THEORY
tions of monophonic compatibility: just as the engineer can state it quantitatively in terms of signal balances, the producer can also "hear" compatibility in his own mind's ear simply by approving of his mixdown as it is played in mono--and who is the buying public to dispute him?
HIGHER
ORDER
MATRIX
So far we have discussed balanced 4-2-4 matrices with or without all-pass phase-shift networks for correcting certain basic problems. In this section we will de-
been in popularity in the last year. Electroscribe gaining very briefly the Electro-Voice matrix, Thewhich has Voice is our first encounter with an unbalanced matrix. would not be appropriate to give more than a casual description of theof system. In many it resembles Since the details this system have ways not been disclosed, theit triphonic systems shown in Figs. 3 and 4. By spacing the decoding at still different points, a 6-dB separation has been obtained between the front pair, while the electrical separation between theqn al rearpo inpair is only about and 1 dB. encoding points at u ne ts along the 0-axis by There is a very valid trade-off here. A listener is more demanding of separation in front of him than behind. Also, there is an "assist" given to the rear pair of speakers by the left and right rear signals existing the front pair. These signals effectively "widen" the perceived separation of the rear pair, and Electro-Voice has referred
to this effect as acoustical
matrixing.
JULY/AUGUST1971, VOLUME19, NUMBER7
There is no
-D......... i . /f_ _-cj_ i_"_ _
z! _
__^
f/ /.J
/_J
/
B
1 _
, 'Xv/['[/_/__-___ 'I _../x'-._
i , l-
/fr--_/_t
c[ '__/ J_ I
SYSTEMS
_'_._
_ [ x
/'_
__
____ L
Fig. 11. Construction of balanced 4-3-4 matrix. 557
JOHN M. EARGLE space. The four inputs can be represented by four equally spaced unit vectors, and their projections on the three perpendicular axes determine the encoding coefficients. A regular octahedron exhibits four pairs of parallel sides, and the four unit vectors normal to these pairs must, intuitively, be equally spaced. (A regular tetrahedron could be used as well for this construction.) By centering a regular octahedron as shown around the XIrZ axes and letting its four unit vectors project on these axes, we come up with a fairly simple expression of a regular 4-3-4 matrix: X = cos 35.3 (B + D) Y = cos35.3(A+C) Z = sin 35.3(A+B--C--D)
(11)
and .4' = cos 35.3(Y)+ sin 35.3(Z) ---,4 + 0.33B q- 0.33C -- 0.33D B' = cos 35.3 (X) + sin 35.3 (Z) = B + 0.33`4 + 0.33D- 0.33C C'= cos 35.3(Y) -- sin 35.3(Z) = C + 0.33.4 + 0.33D -- 0.33B D' = cos 35.3 (X) -- sin 35.3 (Z) ---D -- 0.33A + 0.33B + 0.33C.
(12)
In a balanced 4-3-4 matrix the recovered signals exist down some 9.6 dB in the other three loudspeakers, and in addition each is out of phase in the diagonally opposite loudspeaker. It is doubtful, given the vast majority of musical program material, that this balanced 4-3-4 matrix could be distinguished from a discrete fourchannel system. This matrix may be of limited usefulness since there are few three-channel storage-transmission systems in use today. Three-track tape recorders disappeared long ago, but the 4-3-4 matrix could be useful for, say, industrial exhibitions, where three out of four channels could be matrixed in order to present "fourchannel sound," while a fourth physical channel could be used for controlling auxiliary equipment, projectors, etc. This way, that would gated to an Another
a four-track recorder could perform a job otherwise (and rather inefficiently) be releeight-track recorder (the next size up). interesting consideration is FM stereo. In a
way, FM is the only three-channel medium we have, with its normal program pair and the somewhat limited SCA background music channel used by many stations. Perhaps under the present rule structure of broadcasting, the expressions X and Y in the foregoing equations could be assigned to the normal program pair, while Z would be assigned to the SCA channel. Then, with the addition of an SCA receiver in the home, along with an appropriate playback matrix, the listener would have a balanced 4-3-4 array. It is obvious that 4-2-1 compatibility exists all the way down the line, and only the performance characteristics of the SCA channel would impose limits on the overall performance of this 4-3-4 array. What about even higher order matrix arrays? A 6-4-6 matrix would be equivalent to a pair of 3-2-3 matrices, and we could expect the same balance of energy on playback. A 5-4-5 matrix would have excellent characteristics; it would be as close to a "five-channel" system as one would ever need for reproducing music. Its details have not yet been worked out; in all likelihood the 558
derivation is no moro demanding than that nettlesome problem of determining just where the fifth loudspeaker should logically be placed! CONCLUSIONS Two-channel matrix systems have been examined in detail with special emphasis on 4-2-4 systems. In addition to simple linear addition and subtraction of signals, all-pass phase-shift devices can be used to correct for encoding as well as decoding deficiencies in 4-2-4 matrices, and these networks can also be used to guarantee two-channel stereo and monophonic compatibility. Signal expansion, or gain riding, was lightly touched upon, since it is really a subject of its own, apart from matrix theory.Higherordermatriceswereintroduced,the characteristics of a balanced 4-3-4 matrix were discussed in detail, and we saw how such a matrix could be applied to FM stereo broadcasting. Finally, it is interesting to observe a bit of irony in all of this. As the four-channel era'comes upon us, we are just learning how to listen to two channels with maximum effectiveness. Let us hope that we can learn somewhat more quickly how to make the most of four physicai channels. REFERENCES [1] W. J. Albersheim and F. R. Shirley, "Computation Methods for Broad-Band 90 掳 Phase-Difference Networks," IEEE Trans. Circuit Theory, vol. CT-16 (May 1969). [2] B. Bauer, "Some Techniques Toward Better Stereophonic Perspective," J. Audio Eng. Soc., vol. 17, p. 410 (1969). [3] B. Bauer, "Phasor Analysis of Some Stereophonic Phenomena," J. ,4coust. Soc. ,dm., vol. 33, no. 11 (1956). [4] T. Shiga, M. Okamoto, and D. H. Cooper, "A DualTriphonie Matrix System," presented at 40th Convention of the Audio Engineering Society (Apr. 1971). [5] D. H. Cooper, "How Many Channels?" ,4udio Mag. (Nov. 1970). [6] P. Damaske, "Subjektive Untersuchung yon Schallfeldem" (Subjective Investigation of Sound Fields)", ,4cttstica, vol. 19, pp. 199-213 (1967/1968). [71 J. M. Eargle, "Stereo/Mono Disc Compatibility; a Survey of the Problems," J. ,4udio Eng. Soc., vol. 17, p. 276 (1969). [8] I. M. Eargle, "On the Processing of Two- and Three-Channel Program Material for Four-Channel Playback," J. Audio Eng. Soc., vol. 19, pp. 262-266 (Apr. 1971). [9] M. Gardner, "Image Fusion, Broadening, and Displacement in Sound Localization," J. ,4coust. Soc. Am., vol. 46, p. 339 (1969). : [10] H. Haas, "Ober den E[nfluss eines Einfachechos auf die H6rsamkeit yon Sprache" (On the Influence of a Single Echo on the Intelligibility of Speech)", ,4custica, vol. l, pp. 49-58 (1951). [11] D. Hailer, "A New Quadraphonic System," ,4udio Mag. (July 1970). [121 P. Klipsch, "Stereophonic Sound with Two Tracks, Three Channels by Means of a Phantom Circuit _(2PH3)," J. Audio Eng. Soc., vol. 6, p. 118 (1958). [13] E. Madsen, "Extraction of Ambiance Information from Ordinary Recordings," J. ,4udio'Eng. Soc., vol. 18, p. 490 (1970). [14] "Basic Concept of the Sansui Four-Channel (QS) System," Sansui Electric Co., Ltd., Tokyo; specification sheet distributed at Convention of the National Association of FM Broadcasters, Chicago (Mar. 1971), [15] P. Scheiber, "Four Channels and Compatibility," J. Audio Eng. Soc,, vol. 19, pp. 267-279 (Apr. 1971). [16] P. Scheiber, "Suggested Performance RequireJOURNAL OF THE AUDIO ENGINEERING SOCIETY
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MULTICHANNELSTEREOMATRIX SYSTEMS:AN OVERVIEW ments for Compatible Four-Channel Recordings," presented at 40th Convention of the Audio Engineering Society(Apr. 1971). [17] P. Tappan, "An Improvement in Simulated ThreeChannel Stereo," IRE Trans. on Audio, vol. AU-9 (May-
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June 1961). Note: Mr. Eargle's biographyappearedin the April, 1971 Journal. He is currently Director---Commercial Sound Products, Altec, Anaheim, California.
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