4-2-4 Matrix Systems Interchangeability Eargle by Ty chamberlain

4-2-4 Matrix Systems: Standards, Practice, and Interchangeability JOHN

EARGLE

Altec Corporation,

Anaheim,

California

To a large extent, the two-channel encoded form of one matrix can be "converted" for playback through other matrices. Accordingly, programs encoded in certain "nonstandard" matrices can be optimized for current playback practice. These and other operational manipulations of matrix systems are discussed in detail.

INTRODUCTION:

The first 4-2-4 matrix systems introduced in 1969 were of the "non-phasor" type; the encoding and decoding processes were defined in terms of real coefficients (those determined by additive or subtractive combinations of signals without the benefit of all-pass phase shift networks). These early systems had a common weakness; without the use of all-pass phase shift networks it was impossible for them to reproduce a continuum of sound panned around the speaker array without the occurrence of out-of-phase signals existing in some adjacent loudspeaker pairs. Such out--of-phase conditions are quite disturbing in 4-2-4 matrix systems because the inherently low separation of these systems causes an out-of-phase pair to be within 3 dB of each other in level. The introduction of all-pass phase shifting devices

thoroughly compatible with the present EV phasor matrix. The Sansui matrix has been standardized in Japan (Record Industry Association of Japan, March 23, 1972), and its playback compatibility with the SQ/EV type is limited. The UMX approach of Cooper and Nippon Columbia is the least significant of the three in the marketplace at this time. Its uniqueness sets it apart _from the other two systems resulting in quite limited eompatibility with them. Let us now examine in detail these three matrix systerns noting in particular their design goals, their mutual compatibility as well as their individual compatibility with normal stereo and mono requirements.

alleviated this particular problem (while adding perhaps some of its own), and today all competitive 4-2-4 matrix systems are of the phasor type. There are presently three distinct matrix camps: SQ/EV, Sansui, and UMX. Although they started out quite differently, SQ and EV have drawn closer together in the last year; at least one form of SQ playback is

For our analysis, we will use a kind of spherical noration proposed by Scheiber [1 I] in which any amplitude ratio and phase angle between common signals in a two-channel transmission can be represented by a single point on the sphere. Any point on the sphere can be represented as having an azimuth angle a and an elevation angle j3. a is measured from right to left in the XZ plane while /_ is measured away from the XZ plane alongan arc parallel to the YZ plane (see Fig. 1). For

* Presented September 12, 1972 at the 43rd Convention the Audio Engineering Society, New York. DECEMBER 1972, VOLUME20, NUMBERI0

NOTATION

809

JOHN

EARGLE y

ize certain operations on the encoded signals. For example, any point on the XZ plane can be rotated in that plane any angle a by performing the following operation on the transmissionchannels:

L--jR J t

L'T = L e cos (a/2) R'_ = RTCOS(a/2)

L=I_

+ Re sin (a/2) -- Lesin(a/2).

(7)

{

Applying this operation to the left-right-sum-difference matrix given in Eq. (4) for a 45 ° rotation: LEFT

i//

_ I

L'_ = .924L ar .924F-R'_ = .924R 4- .383F-

I I /

// / / .= -j R

for n-2-n matrices.

given values of a and fl, the matrixing input signal v are: LT (left transmission channel) Rv (right transmission channel) The corresponding ered signal v' is:

dematrixing

equations

(1)

for the recov-

= 90°: L e = .707F 4- L 4- .707B Rv 90 ° = iR + i .707F--]

for an

= v {fl/2) sin a/2 = v { --fl/2} cos a/2. equation

Eq. 4 for/3

sin a/2 + R e {/3/2} cos _/2.

Absolute

separation

separated

by an angle is, in decibels,

between

two

points

the

This operation is shown in Fig. 3. Note that F' and B' are now quadrature related in opposite senses, The term iR in Equation 9 is perhaps misleading. The signal has been advanced 90 °, but since it exists only in Re and not in

sphere

(3)

A simple example will demonstrate this. Let us find the encoding coefficients for a simple left-right-sum-difference matrix of the non-phasor type. The four points will be on the XZ plane (/3 = 0) and will be located at values of a = 0 °, 90 °, 180 °, 270 °. Applying the matrixing equations to each of the four inputs: La = sin (0/2) R + sin (90/2) F + sin (180/2) L 4- sin (270/2) Rv = cos (0/2) R + cos (90/2) F + cos(180/2) L + cos(270/2)

ANALYSIS

OF MATRIX

SYSTEMS

either by specially constructed panpots or specially arrayed microphones which relates each point around the compass to a singular point on the sphere, and it is the loci of these points which we will examine in detail. An-

B B.

,% i -z-"= --:--_:. I

(4)

Le = .707F 4- L 4- .707B R v = R 4- .707F --.707B. the

dematrixing

equation

(5) on

each

= = = =

L -4-.707F 4R 4- .707FF 4- .707L 4B ar .707L-

.707B .707B .707R .707R

I / / _/

LEFT

term

L' R' F' B'

manner,

Encoding signals into a 4-2-4 matrix can be done a variety of ways. It can be done as a continuous process

0 = 20 log 1/cos-_-.

]

}

(6)

Note the "lop-sided" effect in this playback array caused by out-of-phase coefficients between the right and back speakers in this array. The Scheiber spherical notation makes it easy to visualB10

(9)

(2)

By applying we get:

.707B.

Le the shift is of no consequence. In a similar other operations can be constructed.

v' = L, { --fl/2}

Which reduces

(8)

This rotation is shown in Fig. 2. It represents the last Seheiber non-phasor matrix and shows how that matrix evolved out of his original left-right-front-back array. Note that R has become right-front, F has become leftfront, L has become left-back, and B has become rightback in the rotated array. Points on the XZ plane can be tilted about the X-axis by simply operating on either Lv or R_, by an all-pass phase shift network of the desired angle. Applying this to

L---R

Fig. 1. Scheiber spherical notation

.383B 4- .383R .383L + .924B.

Fig. 2. Rotation JOURNAL

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/ LEFT

......

/ ....

LEFT

t / m/

.....

I _

/ /

I \

I '4 I

/ /

Fig. 3. Tilting about the X-axis.

Fig. 4. "Pair-wise"

other way of encoding uses an existing four-track master tape in which signals will have panned between adjacent pairs of tracks, and we will examine in detail the case of signals panned via a quad panpot into the four prime points of the matrix. This "pair-wise" panning [3] of signals poses a difficulty for a non-phasor matrix. Considering Eq. 8, if a signal is panned pair-wise between the rear pair (L and B), then it is obvious that in-phase signals will exist between L_, and RT. This is equivalent to a locus as shown in Fig. 4. Panning proceeds smoothly in the front and both side quadrants, but when the signal enters the rear quadrant, it quickly reverses direction and whips back through the other three! This difficulty and the inevitable out-of-phase condition between one speaker pair have sounded the death knell for nonphasor matrices except in the cheapest of consumer equipment, where their use is intended essentially for "enhancement'' of normal two-channel program material. In general, decoding is done at the four prime ehcoding points. It is not a continuous process as is encoding, and accordingly one does not normally speak of a "decoding locus." However, the possibility of better localization in a "n-2-n" array where there are a large number of speakers, one per source point, suggests that the term decoding locus is not farfetchedf The locus of points for the SQ matrix is shown in Fig. the5. Panning to Rr coversseparation a range on XZ plane,from and LF there is total LF and Rr as given by Eq. 3. Note, however,

of 180 째 between that the

quad panning in a non-phasor

LT = Lr ut- .707 Rn -- j .707 Lr RT = R_ + ] .707 RB -- .707 LB, panned

between

R F and

DECEMBER 1972, VOLUME20, NUMBER10

produce

matrix.

which does not connect via a great circle on the sphere but rather which "wanders" away from the XY plane in the positive Z-axis direction. In a similar manner, the locus connecting Lr and LB "wanders" away from the XY plane in the negative Z-axis direction. In normal stereo playback, an SQ recording will array the L_, signal at the left speaker and the Rr signal at the right speaker. The two rear signals L_ and RB will appear about the center of the two-speaker array. In mono, all four individual inputs will appear at the same level; a signal panned ,front center will be 3 dB higher while one panned rear center will disappear. Signals panned between the side speakers will increase slightly in mono on the right and decrease slightly on the left, this due to the wandering of the locus away from the XY plane discussed in the previous paragraph.

_==--"--_'_

//// LEFT_,

// /

points representing Rn and LR are both only 99 째 away from LF and RF, and this means that the rear signals will be present in L'r and R'r down 3 dB. In a similar manner, both rear signals retain complete separation, while both front signals appear in both L'B and R'B down 3 dB. With pair-wise panning into the following SQ encoding equations:

signals

/ //

_ , _

\\ -C t / /

(10) a locus

Fig. 5. SQ encoding locus. 811

JOHN

EARGLE Y

.'k. :-_

....

Lt,

I I

I /

I I

LEFT

I I

. ;,,

I ,, I ,.

LEFT

109 ° apart

on the

I I

':HT

I I

sphere,

Fig. 7. UMX matrix

The locus of points for the old non-phasor EV matrix was similar to that of Fig. 4. However, the new EV matrix has added all-pass phase shift networks to both the encoding and decoding of the rear pair. Like the SQ system, the rear pair are of equal amplitudes in both Lv and Rv, separation resulting from only the phase angle between them (see Fig. 6). The essential difference in playback between the SQ and new EV systems is that the front pair have been "blended" toward each other as have the rear pair. This results in the new EV matrix approaching what Scheiber has described as a "tetrahedral" matrix [111, one in which the four points are represented by the corners of a tetrahedron nested inside a sphere and exhibiting maximal separation of those four points. If the tetrahedron is regular, its four corare

Fig. 6. New EV matrix encoding locus.

hers

I /

I/_ .F //

and

this

yields

encoding locus.

where the "X's" indicate the primary points. This matrix is unique in that all inputs, regardless of azimuth angle, appear in mono playback with equal intensity. In stereo playback, both right-front and right-back images appear panned in slightly from the right loudspeaker, and both left-front and left-back images likewise appear panned in. Center front and center rear images appear in equal amplitudes (but in opposite quadrature) between the two transmission channels. Far-left and far-right signals result in only the left and right speakers, respectively, being actuated. The UMX encoding and decoding equations for an input v at _any azimuth 'angle 0 ate: 1 + e;0

LT =

2 1 --eJe

4.7 dB separation between any recovered signal and the values existing at the other three loudspeakers. In the encoding function only, EV has introduced an imbalance which results in a pair-wise panned rear center signal being encoded somewhat to the left of the rear center

RT, --

(12) 2

L, + Re

/ LT--R_

of the sphere. In so avoiding coded signal will not disappear

the rear point, the enin mono as program is

panned across the rear, however, signals panned to the rear speakers will appear about 6 dB below those panned to the front speakers. The performance in normal stereo playback is not unlike the SQ system; the front pair will appear slightly panned between the two loudspeakers, while the rear pair will appear disposed about the center of the array. The current EV encoding equations are:

LT = LF-t-.318 Rr+ .549L B -- j.5 LB -¢ .5 RB -- j .549 Rn R e = .318L_,-J-Rr--.725L B -- i. 159 L r +. 159 Rj_ + i .725 RB.

(11 )

Cooper and Shiga define the encoding and decoding of the UMX matrix as a locus of points occupying the great circle in the XY plane. This is shown in Fig. 7, 812

-- --

t- J,,

) e-J o'

(13)

Suppose we encode a signal at zero azimuth angle, it will then be recovered at unity level if we decode at the same value of 0. Now, we can determine the adjacent speaker crosstalk by decoding at angles of ± 90 °. When this is done, we get amplitudes of .707 at phase angles ± 45 °, while performing the same operation for the opposite loudspeaker (decoding 180 ° away from encoding) yields zero. The Sansui matrix has a locus as shown in Fig. 8. Note that it can be derived directly from the UMX by the transformation shown in Fig. 3. In other words, by simply inserting a 90 ° all-pass network in RT of the UMX transmission pair, the UMX encoded tape can function as a Sansui master. In just the same way a --90 ° ail-pass network inserted in Re of a Sansui transmission pair converts it to a UMX matrix. A rather elegant proof exists for this: If an ideal UMX transmission pair LT and Re is converted to the Sansui pair LT and jR/, JOURNAL

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tions in an anechoic environment, the listener would perceive the rear pair of signals panned outside the loudspeaker array. In mono, however, there would be the familiar center-front 3 dB buildup along with a cancellation of a center-rear signal. Also, the rear pair of signals would be reproduced some 7.6 dB lower than the front pair.

- - __ _ I.

/\_'

, ,' J " I / /_ ......

LEFT t

r_,

I !..... t !

// /

TRANSFORMATION TO ANOTHER X

/ --

FROM

ONE

MATRIX

Fig. 9 illustrates the UMX-Sansui transformation we have just discussed. In general, we can convert any matrix whoae locus is a great circle on the sphere to any other matrix whose locus is a great circle. In addition to the tilting transformation shown in Fig. 9, we would need the rotational transformation described in Eq. (7) and shown symbolically in Fig. 10. Thus, a UMX matrix could be converted to a left-rightsum difference matrix by successive applications of tilting 90 ° and rotating 45 ° in the XZ plane. Conversely, a left-right-sum-difference matrix can be converted via San-

Fig. 8, Sansui matrix encoding locus,

sui to a UMX matrix--at least as far as the four prime encoding points are concerned. If it had been originally

then we should expect the L_ and jRT locus to lie in the XZ plane. If they do, then the phase angle between them would always be zero or 180 °. L_ and jR, would be collinear for all values of 0, and their vector cross product

arrived at through non-phasor combination, then it would carry all of its ambiguities through the transformation.

Lv X jR v would be zero. This is, in fact, the case for all values of 0 when the collinearity test is applied to LT and jRT.

L,o

The loci shown in Figs. pair-wise encoding from a they represent continuous would be provided by a

7 and 8 do not correspond to four-track master tape; rather, encoding along ideal loci as special panpot which would

illustrated earlier in Fig. 5) if encoding an existing pair-wise four-track master two cases, however, the wandering is from a pair-wise panned four-track uses the following equations:

LT = .924 L_ + .383 R F + j.924 LB +/.383 RT = .924Rj_+.383Lv--j.383L_--j.924RB.

mas-

RB (14)

We can expect the Sansui encoded master tape to perform in normal stereo very much like a UMX encoded master. However, under very stringent listening condi-

/-r o

eL'7 UMX

SANSUI , .o R r

L_ o

<_ L'r SANSUI

R, o-

_ i

UMX /-9 _°°]

o R_-

Fig. 9. UMX Sansui transformation, DECEMBER 1972, VOLUME

20, NUMBER

oL'r

®b(

.,_._,/' 'x..Af._. _ /cos _ J v- \ '_,_}

1?,o

encode azimuth directly into the appropriate LT and RT. Both the UMX and Sansui matrices would exhibit "wandering'' loci (as were done from tape. In these rather slight, For encoding ter tape, Sansui

'x )c°s e jx,\. -_ 2.., %4,_ _ ._._j

oR_

Fig. 10. XZ-plane rotation. Neither the SQ nor new EV matrix have great circle loci. However, the SQ matrix has prime encoding points which lie on a great circle in the XY plane, and if we ignore panned signals as well as directional assignments these prime points could be converted into a left-rightsum-difference matrix as well as a Sansui matrix. This is not a very practical transformation program material relies on panned specific direction assignments. INTER-MATRIX To what extent

since the bulk images as well

of as

COMPATIBILITY can records

be played over another? all matrix combinations

encoded

for one matrix

We can answer this question for simply by inspection of their

respective loci on the sphere and application of Eq. (3). Consider first an SQ playback matrix. Its front pair are amplitude related and the rear pair phase related. If a Sansui record was played over this system, the left-front speaker would produce a sum of both left inputs and the right-front speaker the sum of bothright inputs. Both sets of images would appear panned in slighted toward the center. Both rear speakers, however, would produce a monophonic sum of the four inputs because all the Sansui encoding points. A UMX recording played each of the rear SQ decoding points is equidistant from over an SQ matrix would produce the same total "left and right" signals via the front speakers as observed with 813

JOHN EARGLE the Sansui record. The rear pair would exhibit a sum of front signals at one speaker and rear signals at the other, Not a very compatible situation; but if we have the freedom to relocate the speakers in a "diamond" array with one of the rear speakers transposed to front-center, then we indeed have a compatible situation. An EV record would obviously perform quite accurately over an SQ matrix since both sets of encoding points are fairly close to each other, Essentially, the same observations for SQ would apply to the EV playback matrix. There would be one exception; when playing a Sansui record, the rear speaker pair would present substantially more rear signal than front, If an SQ or EV recording is played on a UMX matrix, the left-front input would appear equally in both left speakers and the right-front input equally at both right speakers. In addition, one of the rear inputs would appear at both front speakers while the remaining rear input would appear in both back speakers. There is, unfortunately, no possible transposition of loudspeakers to alleviate these problems. If a Sansui record is played on a UMX matrix, both right inputs along with lesser amounts of the left inputs, would appear equally in both right speakers. Likewise, both left inputs along with lesser amounts of the right inputs, will appear at both left loudspeakers. A degree of left-right separation will have been maintained, but there is no fore-aft separation at all. If an SQ recording is played over a Sansui matrix, the left-front input wiil appear at both left speakers and the right-front input will appear at both right speakers. A sum of both rear inputs would appear at all four speakers, The situation would be marginally better for an EVencoded record; there would be a slight degree of fore-aft separation due to the fact that in the EV encoding scheme the two front inputs appear on the positive side of the XY plane and the two rear inputs on the negative side. We should note here that records encoded with the old EV matrix (similar to that shown in Fig. 4) would play back over the Sansui matrix with great accuracy as far as prime encoding points are concerned. If a UMX recording is played on the Sansui matrix, we get the same result as playing a Sansui recording over a UMX matrix, INDUSTRY

STANDARDIZATION

The Record Industry Association of America has issued standards for SQ encoding, while the Record Industry Association of Japan has issued standards for both great circle encoding in the XZ plane (which they call the "regular matrix") and the SQ matrix. The regular matrix, like all great circle loci requires a specially constructed panpot (or a particular microphone array) to yield the ideal results. The Sansui encoding scheme (Eq. (14) comes the closest of any of the proposed matrix systems in satisfying the regular matrix requirements in that the four encoding points (La, Rv, LB and RB) fall on the great circle locus. In the two side quadrants however, encoding by way of Eq. (14) exhibits the characteristic wandering away from the ideal locus which we have seen before with encoding from a four-track source. The issuance of lhese standards by no means implies that the matrix battle in either country is over--only that those record industry organizations have offered to provide 814

guidelines for their members who wish to "experiment" with a given matrix. After all, from a record making point of view all proposed matrix systems are only variations in the "software" aspect of two-channel recording. All the systems are compatible for stereo playback, and they require no changes in the actual manufacture of the disks. Playback is an altogether different problem. Phonograph manufacturers invest many dollars in tooling and design, and they do not want their models to become obsolete before they reach the marketplace. Accordingly, the EIA (Electronic Industries Association), an American association of manufacturers of consumer electronic devices, has proceeded cautiously in promulgating standards for its members. Among the concerns of manufacturers of "hardware" are the matters of monophonic compatibility, stereo compatibility, and simplicity of design. Not too different from their concerns are those of FM broadcasting, itself a two-channel medium. Current thinking among American manufacturers seems to be running in the SQ/EV direction, perhaps because of the significant technical support being offered by both companies and, of course, because of the wide range of program material available. The alternate CBSSQ "10-40" playback matrix is recommended by them for lower priced applications which will not have the benefits of program directed gain riding. It is the standard SQ playbackmatrix with a 10 percent blend between the front pair and a 40 percent blend between the rear pair. This scheme provides a greater degree of foreaft separation than the standard SQ playback matrix without gain riding, and it is virtually identical to the new EV playback matrix. To a very great extent dynamic control of the playback function, whether by gain riding or variation of the matrix coefficients themselves, is equally applicable to all the matrix systems we have discussed. It is safe to say that they can all benefit from some degree of dynamic controls, however, some matrices seem to need dynamic control a little more urgently than others. A number of recordings have been issued in the Sansui format, and they have one advantage not shared by the other contenders; like the older EV records they work on non-phasorplayback matrices since the four prime encoding points are on the XZ plane. The Sansui record presents a stereo array which yields just as much separation of the rear pair as it does the front pair. Neither SQ nor EV can do this, but the price paid by Sansui for this benefit is reduced monophonic compatibility (7.6 dB reduction of the rear pair as opposed to 0 dB for SQ and about 6 dB for EV). In many regards, the UMX is the most elegant solution to matrix problems in general. It is actually a family of matrices, all mutually compatible, and it allows, for an orderly growth from two to three and even four transmission channels. It has ideal stereo and monophonic compatibility, and it suffers only a late entry into the matrix race.

BIBLIOGRAPHY (Note: This bibliography is a supplement to that given in the author's earlier papers [5]. It lists only those papers of significance published or given since the middle of 1971.) JOURNAL

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4-2-4 MATRIX SYSTEMS: STANDARDS, PRACTICE, AND [1] Benjamin B. Bauer, Daniel W. Gravereaux, and Arthur J. Gust, "A Compatible Stereo-Quadraphonic (SQ) Record System," J. Audio Eng. Soc., vol. 19, pp. 638-646 (September 1971). [2] Benjamin B. Bauer, Daniel W. Gravereaux, and Gerald A. Budelman, "Implementation of the StereoQuadraphonic (SQ) Record System," presented at the May 1972 AES Convention, Los Angeles. [3] Duane Cooper and Takeo Shiga, "Discrete-Matrix Multichannel Stereo," J. Audio Eng. Soc., vol. 20, pp. 346-360 (June 1972). [4] Howard M. Durbin, "Playback Effects from Matrixed Recording," J. Audio Eng. Soc., vol. 20, pp. 729733 (Novemb_ 1972). [5] John Eargle, "Multichannel Stereo Matrix Systems: An Overview," J. Audio Eng. Soc., vol. 19, pp. 552-559 (July/August 1971). [6] R. Itoh, "Proposed Universal Encoding Standards

THE

for Compatible Four-Channel Matrixing," J. Audio Eng. Soc., vol. 20, pp. 167-173 (April 1972). [7] R. Itoh and Susumu Takahashi, "The Sansui QS Four-Channel System and a Newly Developed Technique to Improve Its Separation Characteristics," presented at the May 1972 AES Convention, Los Angeles. [8] Ronald K. Jurgen, "Untangling the 'Quad' Confusion," IEEE Spectrum, vol. 9, pp. 55-62 (July 1972). [9] Takeshi Nakayama, Tanetoshi Miura, Osamu Kosaka, Michio Okamoto and Takeo Shiga, "Subjective Assessment of Multichannel Reproduction," J. Audio Eng. Soc., vol. 19, pp. 744-751 (October 1971). [10] Donald Patten, "A Quadraphonic Oscilloscope Display Teclmique," J. Audio Eng. Soc., vol. 20, pp. 483489 (July/August 1972). [11] Peter Scheiber, "Analyzing Phase-Amplitude Matrices," J. Audio Eng. Soc., vol. 19, pp. 835-839 (November 1971).

AUTHOR

John Eargle received the Bachelor of Music degree from the Eastman School of Music, the Master of Music degree from the University of Michigan, the BSEE degree from the University of Texas, and the Master of Engineering degree from Cooper Union. He is a member of Tau Beta Pi, Eta Kappa Nu, the Acoustical Society of America, a senior member of the IEEE,

DECEMBER 1972, VOLUME20, NUMBER10

INTERCHANGEABILITY

and a Fellow of the AES. He is a widely published author in the areas of sound recording and reproduction and has worked in those fields for fifteen years. He has been with the Altec Corporation since June 1971 as Director, Commercial Sound Products, where his responsibility is product development and application in the areas of commercial and professional sound.

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