Page 1

PREPRINT

NO. 904 (A-7)

CHARACTERISTICS OF THE SANSUI QS VARIO-MATRIX BASED ON A PSYCHOAOOUSTIC STUDY OF THE LOCALIZATION OF SOUND SOURCES IN FOUR-CHANNEL STEREO

Part I - CHARACTERISTICS OF THE SANSUI QS VARIO-MATRIX Ryousuke Itoh and Susumu Takahashi Sansui Electric Company Tokyo, Japan Part II - THE PSYCHOACOUSTIC Masao Nishimaki Tokyo Institute of Technology Tokyo, Japan and Kouichi Hirano Sansui Electric Company

PRESENTED 43rd

AT

LOCALIZATION

OF SOUND SOURCES IN FOUR-CHANNEL

STEREO

THE

CONVENTION

SEPTEMBER

12-15,

1972

:

ConventionPrice......... $ .35 By Moil to Members...... $ .75 ByMail to Non-Members...$1.00

AN AUDIO ENGINEERING SOCIETY PREPRINT This preprint has been reproduced from the author's advance manuscript, without editing, corrections or formal review by the Editorial Board. For this reason there may be changes should this paper be published in the Journal of the Audio Engineering Society. Preprints may not be reprinted without prior permission from the Society's Publication Office. Permission does not constitute an endorsement by the AES of the contents of this preprint. Additional preprints may be obtained by sending request and remittance to the Audio Engineering Society Room 929, 60 East 42nd Street, New York, N. Y. 10017. Cc)Copyright

1972 by the Audio

Engineering

Society.

All

rights

reserved.


O_d_ACTERISTICS OF THE SANSUI QS VARIO-MATRIXBASEDON A PSYGqO-ACOUSTIC STUDYOF 71m LOCALIZATIONOF SOl'ID SOURCESIN FOUR*C_L

PAR?' I:

STEREO

f_IARACTERISTIC_ OF THE SANSUI QS VARIO~b2TRIX

By Ryousuke Itoh

and Sustmlu Takahashi,

Sansui

Electric

Co.,

Ltd.

ABSTRACT The dynamic distribution of separation by the Vario-Matrix decoding technique is described with particular reference to the occurrence of simultaneous and closely succeeding sounds from different directions. This operation is related to tile perception of directionality, including directional masking effects with respect to time difference, amplitude difference and even frequency difference.

PART II:

_

PSYU_OACOUSTICLOCALIZATIONOF SOUNDSOURCES IN FOUR-C_IANNEL STEREO

By Dr. Masao Nishin_ki, and Kouicbi

Professor, Tokyo Institute of Tedmology, Hirano, Sansui Electric Co., Ltd. ABSTRACT

1tm mechanism by which sound directionality is recognized by the human ear is investigated, particularly with respect to reproduction in a basic, four-channel sound field. The roles of such factors as phase, amplitude and frequency are studied, and an attempt is made to establish a theoretical basis for the mechanism of perception. PART I

iNTRODUCTION Until today a number of systems have been proposed by different manufacturers to effect what we now call 4-channel sound reproduction. While these systems are being appraised today from various angles, the authors feel a strong need to


return once performance.

again

to

the

very

basic

criteria

of

4-channel

It appears that our question should not just be one of choosing the discrete or matrix system. It should rather be what system, or what approach will guarantee the collecting, storing, transmitting and recovering of the total 360-degree directionality of original sound sources. And what system or approach will guarantee it with no degradation of their tone quality, and at the same time be really practical at the recording and playback ends, as well as in the broadcast station, requiring no dreadfully complicated or expensive addition or modification of the present equipment. Furthermore, to the operators of broadcast stations, it will be of equal importance to be able to transmit the required information in the narrowest band possible. The authors recall the time when RCA established firm theories of chromatics prior to proposing the NTSC color television system, and feel that we too should benefit by an in-depth study of sound directionality before casting our vote on the various 4-channel systems thus far proposed. For this reason, a report on a psycho-acoustic study of the localization of sound sources in 4-channel stereo will be presented in the second half of this paper. 1.

MASKING OF DIRECTIONAL

INFORMATION

It is a well-known phenomenon that, when two sounds exist concurrently, the lower-amplitude sound is masked by the higheramplitude sound. But to the authors' knowledge, no report was made until recently about the masking of one sound by another when they arrive simultaneously from different directions. A recent study, however, has disclosed that the masking of directionality does happen every time a high-amplitude sound and a lower-amplitude sound come in from different directions at the same time. The weaker sound is masked by the stronger one, its directionality becoming ambiguous. Let us introduce the results of one study. This study reveals the process of "backward masking" that takes place when an interfering sound arrives later than a principal sound. It examines how the directional sense of the preceding sound is affected by the loudness of the succeeding sound. The primary experiment of this study involved placing 15 loudspeakers at intervals of 15 degrees each in an anechoic chamber, as shown in Fig. 1, then emitting sound from two given loudspeakers at a given time interval. Subsequently, the directions from which these sounds seemed to arrive were detected as closely as possible.

-2-


From this experiment, it was determined that if the succeeding sound is louder than the preceding one by 10dB, there must be a time lag of 25 milliseconds or more in order for the directionalities of the two sounds to be accurately distinguished. If the time lag is less than 25 milliseconds, the preceding sound and the succeeding 10dB larger sound have been found to mutually obscure their directionalities. It was also discovered that a succeeding sound which is larger by 20dB than the preceding sound would disguise the latter's directionality were it not produced with a time lag of at least milliseconds. The above pertains to the backward masking of a preceding sound, which is less susceptible to masking in the first place. Reports have been received that the directionality of a succeeding sound is much more likely to be masked in a forward masking phenomenon. It has been found to happen even though the succeeding sound is identical to the preceding sound in loudness. While a difference directionality difference

the ordinary "loudness" masking occurs when there is of 30 to 40 dB between two sounds, the masking of has been found to occur with no difference or a as small as 10 to 20dB.

This, however, stands to reason. The loudness masking means that a small sound is masked by a large sound to become inaudible. It could happen only if there were a considerable sound pressure difference between them. In contrast, the masking of directionality only involves obscuring of the directionality of a weaker sound of a stronger sound; the weaker sound does not become inaudible. Therefore it begins to h_ppen when the difference is still small. under

It should be remembered here that which 4-channel sound is normally

In other words, at is producing a sound of obscured directional]ties

such are heard.

the

circumstances

the moment when one of the four loudspeakers high amplitude, our ears are sensing of the sounds from the other three speakers.

To the extent that this masking of directionality happens among the four loudspeakers in 4-channel stereo, the question is posed as to whether it is really necessary to transmit the masked channels as well in discrete form. It is a question that merits serious the consideration of us all in the industry. After all, one always listens to four sounds 4-channel stereo reproduction. It is essentially having four independent telephone circuits.

-3-

s_multaneously different from

in


2.

QS VARIO-MATRIX

One corollary is derived from the foregoing discussion: four-channel effects truly equivalent to the discrete system would be obtainable from a matrix system which continually compares the four sounds as to their loudness levels so that it reproduces the largest sound with the clearest directionality, and the smaller sounds occuring within a certain time lag with less clear directionalities, 'rovp____v!_d_ that such obscuring of directionalities is within limits dictated by the psycho-acoustics of 4-channel listening, which is yet to be studied seriously. The QS Vario-Matrix employed in Sansui's QS REGULAR MATRIX system has been developed on the basis of this corollary. In ther words, it continually scans the phase relationship between LT and RT to detect in which direction the sound is relatively dominant--and how dominant it is--both in level and timing in the sound field formed by the four loudspeakers and the phantom images among them. It then utilizes the information so obtained to alter its own matrix coefficient from moment to moment (with a time constant of less than the 10 milliseconds necessary for the masking of sound directionality to occur), so as to improve the inter-channel separation without changing the output level itself. This is comparable to regarding the level of a sound as a weight, then determining the center of gravity of the numerous sounds placed on a piece of paper, and controlling the matrix depending on the location of this shifting center of gravity. As the center of gravity moves further away from the center of the paper itself, the matrix increases the separation of the sound in that direction. Just how this is accomplished in the Qs Varieblatrix becomes obvious when its separation characteristic is measured by a set-up as illustrated in Fig. 2. Under this set-up, a lkllz signal Js fed to the LF input of the QS Encoder while a 3kHz signal is fed to the X.B input, alternately varying their levels and measuring the separation of the output signals delivered by the QS Decoder. Since the QS matrices in the Encoder and Decoder are botb rotationally symmetrical, only the separation of the ]kHz input signal in the LF channel need be measured to see what would happen in other channels; there is no need to repeat the measurement for each channel. Fig. 3 presents the results of this measurement. The vertical axis of the graph indicates the signal level at the four output terminals of the Decoder after the lkHz signal is fed to the LF input terminal of the Encoder. The horizontal axis shows the ratio between the signal levels fed to the LF and LB input terminals of the Encoder. The right-hand region of the graph 5s where the LF signal is larger than the LB signal, and the left-hand region is where the LB signal is larger than the LF signal. From the graph, it is obvious that when only the lkltz LF is fed to the Encoder, there is separation of more than 20 dB among tbe four channels. As a signal fed to another channel (in this case, a 3kHz signal to the LB channel) increases in level and acquires greater separation, it gradually masks

-4-


the directionality of the 1 kHz LF signal. Consequently, the need for such great separation between the LF and the three other channels decreases, so that the matrix actually reduces the separation of the LF output signal. When the LF signal finally reaches the same level as the LB signal, there remains separation of about 10 dB (or, theorectically, 1]..8 dB). Then, as the 3 kHz signal grows in level, the of the 1 kHz LF signal becomes further unnecessary and tile separation of the 3 kHz LB signal gradually instead.

separation and decreases, increases

There is one important observation to be made here, which is that even the relatively low-level signal retains its total energy throughout this process in the QS Vario-Matrix, rather than being attenuated as in a gain-controlled matrix. In such a matrix, the lower-level signal in the LF channel would no longer be reproduced from that channel, only its crosstalk components being reproduced from other channels. Its total energy is diminished. Were such attenuation of the lower-level signal ever to be permitted from the standpoint of psycho-acoustics, the matrix itself would have to offer the same 30 to 40 dB separation that is required for the natural loudness masking phenomenon to take place. In practice, however, this is nearly impossible. Another important criterion of the performance of a 4-channel matrix is its separation characteristic against two simultaneous input signals. As with the discrete system, the separation characteristSc of a matriĂ— system is usually indicated for a single input signal. However, as soon as some artificial control is applied to the matrix to enhance the separation, it becomes necessary to establish its separation characteristic with respect to two simultaneous input signals. For a matrix system could only be regarded as being able to provide the same 4-channel playback as the discrete system if it offered such separation for two simultaneous input signals that the masking of directionality would occur. eration

The Sansui as Fig.

QS Vario-Matrix thoroughly 3 and 4 demonstrate.

takes

this

into

consid-

It signal rises these

was already discussed before how the separation of an LF changes as another signal enters the LB channel and gradually in level. Fig. 4 shows how the QS Vario-Matrix responds to two different input signals under such circumstances.

Fig. 4-a. illustrates the matrix vectors of the QS Vario-Matrix when the LF signal is of a sufficiently higher level than the LB signal. The matrix vectors of the RF, LB and RB output signals are entirely opposite to that of the LF signal. It follows that, theoretically, no crosstalk appears in the three channels and the separation between tile I,F and the other three channels is infinite. Then, once concurrent signals of identical levels enter the LF and LB inputs of the encoder, the same matrix responds as shown in Fig. 4-b., where the theoretical separation between the LF and LB channels is ]1.8 dB.

-5-


Furthermore, when the LB signal is sufficiently higher than the LF signal, the matrix changes as shown in Fig. 4-c., so that the separation of the LB channel from the other three channels is infinitely large but that of the lower-level signal in the LF channel becomes monophonic. These variations of the QS Vario-Matrix are easier to understand if one considers the output characteristic of the QS REGULAR MATRIX itself as illustrated in Fig. 4-d. The solid-line curve in the graph represents its output characteristic with respect to an LF input signal. By automatically altering the matrix coefficient, as in the QS Vario-Matrix, the separation of a given point from the LF signal undergoes a change as indicated on the graph. The dotted-line curve represents the same characteristic regarding a signal in the LB channel. The QS Vario-Matrix thus exploits the peculiar properties of the human auditory sense reviewed earlier in this paper. In short, it takes advantage of the masking of directionality and, while preserving the total energy of each input signal, provides a 4-channel sound field which embodies the most important virtues of the discrete system.

3.

TltE SPLIT~BAND

_S VARIO-blATRIX

From the foregoing discussion of the masking of sound directionality and the characteristic of the QS Vario-Matrix, it should be understandable why this matrix provides aurally sufficient separation among the reproduccd four channels. And in actual listening tests, it has startled many a doubting engineer. But hopeful of still more improvement, we set out to see if we could not better profit from the directionality masking phenomenon. What we eventually did was to screen the decoder input signals into low and high frequency bands, utilizing a filter. These signals were then processed through separate QS Vario-Matrices for separate control of the matrix coefficient in each hand. This additional technique, which we call band splitting, improves tile separation against two simultaneous input signals to such an extent that it is practically the same as when only a signal enters the encod2ng matrix. 4.

THE FUTURE OF 4-CIIANNEL

STEREO

The Sansui QS vario-Matrix technique we have preceding paragraphs, while it is a matrix system, degree of inter-channel separation that is aurally from that of the discrete system.

reviewed in the has given us a indistinguishable

Let us now turn to a very fundamental question icant bearing upon the future oÂŁ 4-channel stereo. utilization of information-storing and transmitting a very interesting analogy to the process leading to tion of the color television system.

having a signifIt concerns the space, and has the standardiza-

In the earlier days of color television, it was generally believed that color television _ould require a frequency hand three tSmes as wide as monochrome television. Since the latter utilizes 6 mhz, this meant a frequency band of 18 mhz was necessary.

-6-


However, RCA then came up with authentic theories of chromatics, demonstrating that no harm would be done by broadcasting only the principal area of the picture screen in color while transmitting the small, unessential areas in black-and-white. This was a major discovery that eventually led to the use of 6 mhz for color television as stipulated by the NTSC or PAL system today. No viewer has yet been heard to complain that small areas on his color television screen were without colors. The authors wonder whether the same logic would not apply to 4-channel sound reproduction. And it is this line of thought that is behind our proposal that a relatively strong sound be reproduced with distinct directionality, while simultaneous weaker sounds are reproduced more or less monophonically. We on our part are aware that more advanced theories need be established before we are thoroughly able to substantiate such a proposal. When the broadcast industry started to contemplate color television, it had already been known that all colors were separable into three primary colors, and that any color could therefore be reproduced on the screen through the use of three transmitting spaces. To our regret, however, today's psycho-acoustics has not even given us the answer to the msot basic question of how many channels are really needed to transmit the complete 360-degree directionality of a live sound field. Had the same kind of ignorance been prevalent in the initial stage of color television, it would have been asserted that, to show a rainbow on color television, called for 42 mhz (6 mhz times 7) since it consists of 7 colors. Hence it is our contention that the question should be studied, with extreme care at the present stage of 4-channel stereo technology, whether four separate spaces are really necessary to store and transmit the information required for 4-channel sound reproduction. Otherwise, a great deal of research funding could go down the drain, and in broadcast, bandwidth could be wasted that might be put to other important uses. 5.

CONCLUSION

It is not precisely are really required to in a live sound field.

known at the present time how many channels transmit the total audio information generated

Should all the required channels to made available, it is still not necessarily guaranteed that sound reproduction of a phenomenally better quality than the present systems utilizing two or four channels will be obtained, especially in view of the peculiar characteristics of the human auditory sense, such as the masking of directionality. Se attentpts psycho-acoustic 4-channel matrix

were made, successfully, to take advantage of such phenomena in the design of a practically possible system employing two channels. The resultant matrix,

-7-


called the QS Vario-Matrix, provides separation of more than 20 dB between any pair of channels against two or more simultaneous input signals, producing aurally sufficient sound-field effects. It is nevertheless undeniable that psycho-acoustic studies of the sound field information are gravely underdeveloped and need closer investigation in the future, if we are to further enhance the quality of 4-channel sound reproduction.

i__l

2 meters

Fig. l


? v 0

'_._o".I _ osc

3 kHz

%0t,._p _,_d_

I Fi9 2

LF input =1kHz

( Measured at I kHz) LF

0 -

LB input=3kHz

.-_""'_

................. _;_,..0

_,.,, ,_._........................

. ,-_

-lo

dB

_? ,:'_.

dB

_.,_,.,

LB

_

-30 _ -30

I

I

-20

I -10

dB

f

_ 0 LF/B

Fig. 3

RB

I

-_

*10

'_'_t,_,

I--_-30 +20

dB

oo


LFI

LF /j/l/

(a) _LB

LF

/

_'" _,,i__ RF <Z\,_--_ RB

Lee

CF

CL

CR

////

RB

LB

LB

(c)

(d)

Fig, 4


PART I I

1.

INTRODUCTION

It was pointed out in Part I of this paper that there exists a definite need for studying the psycho-acoustics of sound reproduction. This Part II is an endeavor in that direction, Jn that it has as its purpose the investigation of the mechanism by which sound directionalities are determined in a basic four-channel sound field. First of ail, it is clear from the structure of the human head that, when a sound source is located directly in front of the face, the ears naturally sense identical sound pressures with identical phases (or arrival times). By the same token, if a sound source is located in a direction other than straight ahead, the sound pressures and phases experienced by the ears are naturally diffe.rent. It is thus generally known that the human ears sense the directionality of a sound source as differences in sound pressure and phase of the sound waves converging upon them. It has not been ascertained yet, however, whether the sound pressure or phase difference is the decisive factor, or how the two interact in deciding the directionality. A simple experiment gives us some insight into this matter. Suppose a pair of speakers are placed to the left and right in front of a listener. Then, sound is reproduced under two conditions:

two

Condition speakers,

a: Feed signals of keeping them in phase

Condition b: speakers, keeping

Feed their

signals levels

identical frequencies but changing their

of identical identical but

to the levels.

frequencies to changing their

the two phases.

Fig. produced I shows, at under condition a, the potentials ( La, As ¢Rb) the left and right ears velocity possess different phases, so that the directionality of the reproduced sound image shifts toward the louder speaker. Under condition b, however, the velocity potentials (¢Lb, ¢Rh) produced at the left and right ears have identical phases and only their magnitudes differ, so that the directionality hardly moves off the center. What this means is that a difference in the intensities of the sounds from speakers is sensed by the ears as a phase difference, whereas a difference in the phases of the sounds from speakers is detected by the ears as a difference in sound intensi'ty.

9

-


It may therefore be said that a phase difference is the primary factor in determining the directionality frequency sound source (approx. below lkHz), as the sharply directional for low-frequency sounds.

at ears

the ears of a loware net

However, for a higher-frequency sound source whose wavelength J s the same as or shorter than the distance between the two ears, a sound pressure difference seems to he a more Lmportant element. This is because any phase difference at the ears will then be greater than 180 degrees and no longer sensed by them; the directionality of such a sound source is merely felt as a result of the directional sensitivity of the ears. Of course, the directionality source is likely to be decided and sound pressure differences

of a middle-frequency by an interaction of both perceived by the ears.

sound the phase

Hence, it is the underlying proposition of this paper that a phase difference at the ears is what determined the directionality of a sound source whose wavelength is longer than the distance between the ears (which, in frequency, roughly means lk}Iz or lower). In the following paragraphs, the phases of a sound source sensed by the left and right ears are first computed in terms of velocity potentials, whereby the directional angle of the sound source is determined as the angle at which the difference bet_een those phases disappears. To put this more simply, assume a man facing front is listening to the sound from a speaker located to his front and left. The phases felt by the left and right ears are naturally different (see Fig. II). Then, as he turns his head to the left, the phases become identical at a certain angle. This counter-clockwise angle, 0, is obtained when he squarely faces the speaker, and is defined as the directionality or directional angle of that sound source (in this case, the speaker). The same logic is then applied to four-channel duction to see how the directional angle of a sound affected as the phase and sound pressure in each of speakers vary.

2.

THEOI_tiT[CAL

BASIS

FOR

sound repro-. source is lhe four

SOUND DIRi!CTIONALITY

We seek to learn theoretically the mechanism by which the sounds from multiple speakers come to give a sense of directionality to a listener seated at a given position. For this purpose, however, it should be first studied experimentally how the phase and sound pressure differences at the ears, and an interaction of them, influence man's directional sense.


Only then can we compute the magnitudes and phases of the sound pressures generated at the ears when sound of specified sound pressure and phase is radiated by multiple speakers. Those values then will be substituted in the formulas derived from the experiments, to ascertain the directionality of the original sound source. Of course, in so doing, the directional sensitivity of the ears, as determined by the head and conchae, should also be taken into consideration. Now, suppose n_ speakers located arbitrarily are emanating sounds of identical frequencies but of varying levels and phases, with a man seated in the middle facing a given direction. Then the total velocity potentials at the left and right ears are given by

_,h,:/, . i n- -iT 2 smil,:-Jr-i

2 _.,_ok

_^,a(,o ,

[ i ]

,=1

_L,MI<.2= -tl ) _,, +J) ,,u;,_k _51:/-a D . s _': 2 ' ' i=]

_

ri [. 2- slnJ_[

._iI((2:-

#,! .-j(rJ,

'fi..,i,:)k

[

]

2

i=l

where

4_]ki

= the

ri

distance

of

the i-th ears,

speaker

coefficient K(2_-ei) for symmetrically,

between

the

the

to

of the

ears

i-th

speaker, the

complex

velocity

potential

at

the

left

_R

= the

complex

velocity

potential

at

the

right

(_i

= the the

counter-c]ockwise angle center-front direction,

=

phase

the

sound

pressures

i_, ,,,o a

Po = the = the

constant,

J"'.""_"

atmospheric angular

in the

(D<< ri),

= the

the

middle

the left ear, right ear, as

_L

k

where

velocity

from the

= the directionality which case it is ears are located

D _ the

Then as

volume

= the distance point between

K(Oi)

pressed

complex

of the and

J-th

eardrum, eardrum,

speaker

from

2_/X. at

the

left

_"' '''째 ,_

J'""'_("

density,

and

frequency.

]1

-

and

right

ear's

[

3 ]

are

ex-


These sound pressures potentials are determined.

can

be

thus

computed

once

the

velocity

There are two difficulties, however. First, the relationship between the sound pressure difference and the phase difference at the ears and the directional sense they perceive has not been experimentally elucidated as yet. Second, sufficient data are not available on the directional sensitivity of the ears. qualities

figures [ 3 ]. results

In

each case, the is the reason.

difficulty

of

measuring

Admittedly, once these difficulties are could be obtained by applying formulas For our purposes, however, we propose by making two assumptions:

those

intangible

resolved, precise [ I ], [ 2 ] and to approximate the

(1) That the directionality of a sound source is determined for the most part by its middle or lower frequencies (approximate]y below lkHz). That is to say that it is determined by the phase difference at the ears. (2) That the directionality of a sound source is the angle at which the phases at the left and right ears become identical as the listener turns his head. This is in spite of the fact that it should ideally be defined as the directional angle of a single sound source at which, when that single sound source is located in a given direction, the same phase difference is perceived at the ears as was perceived of the sound source whose directionality is being sought. 3. APPROXIMATION TtlEORY ON THE LOCALIZATION IMAGE IN A FOUR-CHANNEL '2-2' POSITION

OF A SOUND SOURCE

The following analysis is based on the assumption speakers are placed in tile four corners of a square, as with the listener positioned at the dead center. It is that the center-front direction in the figure is where that sounds reproduced by the speakers are identical in different in level.

[ 2 ],

Then, substituting the the velocity potentials O,

I

_id,[AL I

r _Jrl,[AI

s-i,k_{[Aml.

assumed values in at the ears are

"_''_( ,_'') '

il) k

I :J 2

A,.

? _(c,.,tl ,.dl)

,

cos.__2Dkz. ({ost

AE

_

]

M Il/

_

(A,m

[

12 -

formulas given by

jD

-

4

Al _0co_2)kg(cosJ

........

}

that four in Fig. IV, also assumed 9 = 0, and phase but [ 1 ] and


and _,ilt

1r c_jrk(Ai,E _ )1) _,,,,,(',,"):A,,, I _ j'?_',,-(,,,) D/ ^..... j ) I,,,,,(; ) I) : , A...... :?,_O'(T_'] A,ii)cos2,/2(cos/

k(

,{:^,, ?k , Aim)sln,),?2(cos/

where

4_ALF

= the complex speaker,

s,n#)

sm/t)

(Anl

.'\tl.)CO_,,_,2/.(tr>sO

(Am

AllO,sln2x/2(cosI

J

.......ql[

]

volume

velocity

of

tile

left-front

4_ARF = the complex speaker,

volume

velocity

of

the

right-front

4_ALB = the complex speaker,

volume

velocJty

of

the

left-back

4=ARB = the complex speaker,

volume

velocity

of

the

right-back

r = the

distance

from

D = the

distance

between

k = the

phase

constant,

0 = the angle, from bisector of the Hence, the m.agnitudes and right ears are, ,¢, i hi,d (_o_//

the

Aim)<os (,M,

dead

center

the

ears,

2_/X,

and

to

the center front, line between the

of

_._/{(^,, sm /)

the

: A,,)sm

velocity

,)k

2 y/2 (cob

fJ

of the ears.

potentials

sm/O

speaker,

vertical at

the

left

Dk ^1 I:)Clm2 _/ '2

MI1/I) ' f/\Jll

2 ¢.?to,t/

each

(A.,

Al .)s,n,,D,

k

m

......... 'T

[6 1

and the phase angles 9L and PR of the velocity ears as measured from the middle point between

51

tan

(All

l)k AtiH)_]n2_i2(cost

L (All

l)k Al.)Ct>S,2<2(cc_s

(.Stl c.

from

tan ' (All

.'\l{.)cos2V,

_m/I)

(,\1<_

)k ,\l,ll)hln2,,2(t¢3_]

smtJ)

t,\l.

Aiid{a_.2

/

I)k AIIIQSlIL!_ 2(CoSI] Dk 2i_l.s]

potentials the ears,

at are

the

sm/Il

I)k /2(tos l)k _ [!(tos!

Mil/I)

(:\ltl

^Ill)SIll,2

[aH/l)

(ALII

I)k Al i,)¢os:! x :) (CON

_mo)

[

7

]

SIll//) M II//)

[

8

]

which s',.

_"

[9]

It is already assumed that the directionality of a sound source image is the directional angle (O in Fig. IV) of the vertical bisector of the line between the ears, when the phases at the ears coincide. This O is therefore obtained by substituting OL

=

PR.

- 13-


So,

substituting

PL

PR in

TM

formulas

)

from

[ 7 ] and

[ 8 ], f

l0

[ ll

]

(which means,

if

Dk

we have

1

which Am_ l\.m

Dk sm ...._ l)k

- Ai,m_ /M 4_

When Dk____

_

it

in Al

Let critical

I

l\1_1_

sm/O

, namely

2v-z<< 2

substituting

(c_s/

...... _. (__,J ....,)

X

, f((

coM!

SlnlJ

D ((

I

rani/

r

us now derive the directional points from equation [ 12 ],

into

Sound Pressure front Each Speaker ARF=ALB=ARB=O '

RF only

ARF_0,

ALF=ALB=ARB=0.

LF=RF only

ALF=ARF_0, ALB=ARB= 0,

Input

into

following

__E =45o 4 _

_r=_45 o 4 0=0o

eight

Sound Source Directionality' 45e .45 o 0°

ZS__= 90 ° 2

AEF=ARB=0 '

Table

angles of the an example.

Sound Image DirectionalityO

ALFa0'

ALF=ALB/0 '

as

1

12

1

LF only

LF=LB only

D = 15 cra,

1.6 kHz),

Table

Input

×

V-z

90 °

2

Sound Pressure from Each Speaker

Sound hnage Directionalit T a

LB only

ALB/0 ,

ALF=ARF=ARB=0.

h=-4S

RB only

ARB_0,

ALF=ARF=ALB=0.

-_=45 °

-135 °

LB=RB only

ALB=ARB_O

AiA:=ARF= 0.

0=0 °

+_180 °

RF=RB only

ARF=ARB_0,

ALF=ALB=0.

--_=90 °

Tables 1 and 2 show the that the directional angle of coincide with the directional sound field.

°

Sound Source Directionalit}_ 135 °

-90 °

computed results, Table 1 demonstrates the reproduced sound image does indeed angle of the originat source in the live

14 -


Itowever, Table 2 shows that the reproduced sound image d_rectionality deviates front the real directionality by exactly 180 degrees. This is because, if the listener squarely faces the sound source, and if another sound source is located directly behind him, there is no difference between the phases felt at the left and right ears. So the ears cannot distinguish between the front and back directionalities. Thus, listed image

tions duced

when a sound source is located in one o[ in Table 2, the theoretical directionality shifts 180 degrees.

the

four direc_ of its repro-

In actual listening, however, a listener facing front is naturally able to sense the left and right directions, or the plus and minus of the reproduced directionality 0. Then when the sound source is located at the center back, he normally differentiates between the front and back from experience. If the frequency of the sound source is high, the directional sensitivity of his ears facilitates detecting the dif拢erenee. Next,

let

us actually

apply

this

theory.

Suppose microphones l, 2, 3 and 4 are p]aced in almost identical locations in relation to a relatively distant sound source, as illustrated in Fig. V. Further assume that each microphone possesses cosine directional sensitivity, and that their outputs are to be separately amplified and transmitted and then fed to the LF, RI;, LB and RI3 speakers. Under this assumption, if the distant sound source (which, for our purpose, provides a 'Front input signal') is located in the directional angle 8' from the center front direction, and if it is within the front quadrant defined by the maximally sensitive directions of microphones 1. and 2, then the inputs into the hF and RF speakers tively. equation

are proportionate No input signal

Therefore, [ 12 ],

to cos (--_-g') and cos (__+0'), enters the two back speakers.

substituting we have t

Anl

,\l n

Consequently,

wMcb

means

/

co_,(

tan_/'

{

]

these

n')

O

I

ti')

O

[

values

i _/f

t,

s

ti'

in

I

the

left

respec-

member

of

UHle] '

tan//

g = 0'.

It follm_s that the directZonal angle of the sound source, as viewed from the microphones, matches that of the reproduced sound image heard at the center of the four speakers. And the same holds true for a sound source orkgi, nating in any other quadrant.

15

-


Conversely, given direction, quadrant of Fig. the

signal

cos

(-_+e),

to

a sound image call be say e. For instance, V discussed above, it

the

LF and

feeding

no

RI: speakers

signal

into

at the

produced from a signal ill any if the 0 is inside tile front is only necessary to distribute the

ratio

back

4. WHEN TIIERE IS CROSSTALK TO AI)JACI!NT _PEAKER POSITION

of

cos

(_E_ 0)

and

speakers.

CtIANNELS IN A FOUR-CIIANNEI,

Let us now exami,ne how the Foregoing analysis applies to a four-channel system having two information-transmitting channels and where crosstalk to adjacent channels is unavoidable. Assume a case where crosstalk, as determined coefficient c, exists between each channel and its and where the Four speakers are operating in phase

by crosstalk adjacent channels, with one another.

From formulas [ 4 ] and [ 5 ], the complex volume velocities of the Left Front, Right Front, i,eft Back and Righl. Back speakers are 4_Ai.,F, 4_ARF, 4=ALB and 4_ARB, respectively, if there is no crosstalk among the channels. To simplify tion, however, we'll divide them by 4_ and ARB as the complex volume velocities. come

Then, if there to have complex Left

Front

Right Left Right

crosatalk as velocities

speaker

I:ront Back

is

volullle

assumed of

above,

the

four

speakers

ALF+CARF+CAIB,

speaker

=

speaker

Back

the process of computaobtain Al,i: , ARF , ALB and

Ai_F+CAi_F+CARB, ALE+CALF+CARE, and

speaker

ARE+CARF+CALB.

tlere, we again define the directionality of a reproduced soundsource image as the directional angle at which the phases at the ears become identical, as measured from the center front. Then the relatio: ship between this angle 0, and those complex voJume velocities can be derived by substituting those values in equation [ 12 ]: (l\l

i

( .'\,t

{/\1,,)

(Al/ti

I Alii

cAI

u)

Al F

.\lul

I

rani]

]'he end result is thus identical to equation [ 12 ]. Which means, if a listener is positioned at the dead center of the square formed by the four speakers, the directionality of the reproduced sound image remains the sallie as when no crossta]k existed, so long as the cross talk from each channel leaks to its adjacent channels in identical proportion_ and in phase.


Now has

been

sound

that

tile

pressures To

stitute

directionality

confirmed

to at

the

determine

I_,l,]

[

I!ml

r1 I(AT_

]

in

Then,

if

there

is

crosstalk,

the

ifil _ ") '_'

The sound represented

(At i

,,\ri,

2, A[i _,'Ai_i*)cosL I)k Ar.)c_s, - . 2_(<osf/ sm.) IJk . ,'\p ii) c,Js,! . 2 ( ,s )k , (.,..

\,.)_,.,

pressure by the

the

the

the

ears,

we

sub

is

I¢[.

_

]:

At.)

velocity to

)k '2<Al n)c_)s,_2, (_o_,

) Alu_)to%2 ¥ '! (cns Jsmn)

(Aln

image

how

potentials

its

counterpart

withoutY

I¢10, is

2_,Xm

I 2t(A,,

at 6

(A,i

ratio

/\u*

(,Mn

[

sin/l)

of i. ts

(Al i

(knl

sound

examine

[ ]S ]

magnitude

cros_talk,_

I&L]= ICRI_

us

_,,,)}

cos V 2 (c_ 7

when

potentia]s

equation

I)k Alu_)_os2_/2(cos

I_k.

reproduced let

vary.

ve]ocity

10

the

unchanged,

ears

the

equation

o{

remain

at each second

sm/;)

I)k ,! (co_//

_l.//)

MIl{J) (Al I

3k .\llll)COS212(coMI

_111/1)

_,..>

.,\,,,)_._,.... I)k_o_

,,w,)

ear term

(A.,

therefore of the

right

[

increases member

by of

16

the the

]

amount above

equation. If again ARB

the

used

micro'phones to

pick

up

these

assume

!0h)

Then

tile

other c

=

the

ALF

,

are

ARF,

ALB

and

in equatJon

[ 16 ],

)k / 1' ;! ((.os/] Sill// cob2 · '2(Cos _nnf}) I '!< )k _'2(' si/ _mu c,,s2 (2(co_n stnn) )k ¥ 2(('oq{J _bll/J{oh, /2 (cos/] Mn/l) )k _/2(c,,_/I sm0)c,>.,, 2(t'_'_ sm/;)

and

If

sensit4vJty

signal',

J

values

sound

location

In

directional

input

0

these 10b

Front

cosine

'front

values:

At Il: Al/.

Substituting

with a

words, i

tho

When 0 = ___ ,

-3

I0, ,?h,

increases Left

,,hen or

4

pressure in

Front

0=0, dB,

:ii',

then

.... ';'

_ 2_,,,,l>k 2

-

at_ speaker

17-

._lLt,'l_,d}_)

for can

instance, he

computed.

the

Center


For If

as

c

the

5.

_21

a sound or

(

Fig. VII crosstalk

4-2-4

source

klB)_

j6jj_ic,

whose

2 Il

shows how changes.

MATRIX

frequency

is

I__ <<

__.

,

-i._

1 ,

(7 t6dlI)

tile

sound

pressure

in

each

channel

increases

SYSTEMS

Any two-ctlannel matrix system produces a please difference of 180 degrees as it tries to matrix a complete 350 degrees of sound. Diffcrent systems havc been proposed to date which differently distribute this phase difference and the inevitable crosstalk. Fer our purpose, it will suffice to study the localization of a seund image in two representative systems which are already in practical use

.

(1) A Matrix System Which by +90 © and Which Distributes Symmetrica] Fasi_ion.

Fig.

Such VIII,

a matrix with each

system speaker I.l: RF I,B RB

Substituting Formulas left and

thesc [ 4 right !51

dc]ivers generating

b- uXJ m _ \m I;- (,\m _ALi Ix (,\] , c'/lm_ l-(,\1¢: _ \EI_

values

] and ears,

Phase-Shifts the the Crosstalk

in

;_ j_ l, ),

the

the

tAM

jc.\llOCO_

output vectors as shown a complex volumc velocity

place

of

2_ 2 ) c_l_ll

Al.F,

ARF ,

potentials

l_Am

, \kl kl)

%till/)

(\ill

J_AlUOStn2_

tc_S¢ _ _9[(°s//

,in?i)

C \ti kD 12t_c_/I

jl \11_ ,

J, \1

.lll//i

jl \11

, \Ifil

J)

_U_S,> - % 2'to_/

i

\1_1

_tl/lll

t ,\II'

J, \ti _[ll//)

,AHI: kI)

J_Ln _ _ 2(t_*_d j( 5[_h

_[ _

jr,\ill

stCld / Jc-xlJ:_ blt_//} Jt B[i )

kD

s

)[i. (._1

( \l{t [)

j t:\l

[

i At i L _ //

lC,\tH i

_,\ ....

(,XH[

i Xl [*_l'_)_> Hob / .ill/I} -'2 kD k) ! ,) (t<)h/I _lll//) tL \t*l I) _11112) ([ \Il 5 b I > ( (t)st/ _lll/l_

\II/CO_> I .\t_t

\,,

.XHH

\1 i_ t .\l:l*/Co_

.\lin

:\ ....

kl) ((c)h) i ._l )_lll,i

x,,:).....

_tn/)

_l,\ll

) ) cost/

_")_o_,,

.\l;h

\1 i

to-,, kD )(tO_

stn//)

Sill/J)

.... ,_

}1

18

-

[

Ai, B and

perceivcd

kI) _Lll 2 I)k _ '2 ( _*_//

by ei'

\1 n} .\m_) ,\L I_) knJ_

[ 5 ], the velocity _L and _R, are

_r -.k( (Att

Rear Channel Signals in a RotatJonally

18

]

ARB in at

the


and ik _,_t_

_

kD

_ All

, (Am'

- _,Al_l

cAH

(Al I

sin/} ) A_ .)cos

/'/\Iii

,(A.,

, cAN0cos; k)

! cAm0cos2_

Al,.

k) i<sln,jl/_(Cosl/ , /{c(Alu

r A..

i,(/\l

/ _

cos//

(cos//

sm0)

[ sm//)

_,(Am

.

/ "\u.)

kD / AliB) Slll2x/2(cosY;sln/l)

i

2kD d 2 (cos ,

Ali.

2 '/2

sine) kl)

Alu0

c(Aii

iAI,I)snl.).7__,, (cos//

s

cos 2 kI) d 2 (cos[/,

sm/t)

It/

_A,,. A,.,, ,A,_,0_,%.,2(cos. kl) _._//)}_

[ 19

]

Let us now see how these formulas apply to an actual record_ lng situation involving a 'front input signal.' where a signal enters only the Left Front and Right Front microphones. Since

ALB=ARB, substituting

them

s I_ L cAl,i,

( A,a. _ A,, kl)

)c.s

bill 9..x) 2 (c°s(t

, sill/J)

jQAIm'' [ cAlu

C/\ltl

kD ) mn 2 _/2 (cos#

"At"'"ts2,,/2 kI) _:°_'/'

in

I) 2 _t 2 cos

the

sm0) kD s

sin/t)

.... /ii ,,'a_,t

(Alii'

_x,6'2 (cos_J (Alii'

r tala')

..... ,,kD 2(co_,/_,

above

two formulas k) / _(cos//

i cAi.t')cos2_

' sm//)

Sill//) k ) sln2 _v2 (cost/

Mn/J)

.... ,) }1

[

20

]

id, 0m_

? r

_(l\m ,

cA"')c°s2

_/2 (cos # k])

sm_/)

(Am':

cA,_)cos_,/2(cos# kl)

, sm/l)

....../D(........,)., ....... ?]:,( .........) /{(Ali cAlll')slll2 CALl (oh

To

simplify

the

kl) '/'2 (COSt/ SI/

computing (All c/\Il (,'\l_ (All

Formulas

[ 2 [ kl)

kD c,'\ld)cos,>~_/2cos m kD s_12,2(cosO

sill//)

Ii

sm[/)

sm/0 c:\m sm//) tam

[ 21 ] can

:/_"((_, ,,),¢.

(/\Ill'

cAl,I )sin 2 kI) v/2 lc{m//

c.X}{} CO_[_kD 5/ 2 (_OSl/

Sill//)

......)})

[ 21 ]

process,

kD cam )sm L /2 (cost/ kD cos _ '2 (co_ll slnr/)

[ 20 ] and 0,

sill//)

(/\m

cA_j)cos)2_2/

kD

(cos/t

sln//)_a

kI) sm2c2(cos// (Am

sm/I)' h , kD c"\ml)sm2 _/2 (cos//

cos kD 2 ('

then

sit

sm/t)

be rewritten

d)_

[ 22

_,_,:/'_((,,,,),(_,_))

.c

smt/)r=d

as ]

[ 23 ]

19

-

yields


Accordingly, tials, as

the phase angles oL and PR of those measured front the midd]e point between _-_ t,._-_ac

velocity the ears,

potenare

[ 24 ]

d{ I

and

!'1_

Recalling image is

tan- I

that the directional obtained when PL=PR, c

d

can

be

angle

9 of

the

¢Id

_.l; which

[ ZS ]

{_,,_:' b

[_

as

,,_ua Substituting the original [ 27 ] and rewriting it, _(/_ll!:2C\ll

_l:l)Mrl

[ 27] values we have icl) z2(co_f/

sin/J)

of

a,

] / ' ,_ AiH-

,..,,.......... ) A,,,,)<, ,

x sill

Then the and right ears

_/?

magnitudes are !,_I

sound

[ 26 ]

_, b

rewritten

reproduced

of

tho

velocity

b,

c and d in equation

:_cAiiAiii) ,

k)

)[

_t

potentials

].:(.[b)_ (,, a)_ r

[ 29 ]

16.1 r ] FCab)__]_,,0'

[ 30 ]

] at

the

left

and

As the LB is phase-shifted by +90 degrees from the LF, and the RB by -90 degrees from the RF, it is expected that the ve]ocJty potentials at the left and right ears are different in magnitude. To compute the ratio between the magnitudes,

/

- 20 -


Of course, then b=d=0,

if c=0 whereby

(i.e.,

no

crosstalk)

as

in

the

discrete

system,

2;',, I =l I_hd

Next, Therefore,

for

a

sound

equation

_(A,

[

source

28 ]

which

is

further

(a)

ALF=ARF

,

Au, z 2(1

_ , Au,.'9:

1 sm o ) - 2(Am. ,'A

2

F sin,

sin _.Ă&#x2014;.

)

[

32

]

[

33

]

c_

TIIE

er

lan,

DIRECTIONAL

ANGLE

0 AND VELOCITY

-3dB;

Since ALF2-ARF2=0, we substitute 0=tanO, from which 0=0.

obtain

kD

24-Z<<-z'

kD (cos0

2cAi,iA,r)

kpsh,,

,'

A,i.. _ 2c i 2c:)A,_A,,

FOR

and

is

as

OF COMPUTATIONS RATIO

When

o

2c'")A

rewritten

(I , 2c)(A[jp

EXAMPLES POTENTIAL

I(1

frequency

becomes

k3 /_(cos

124 2cA,.iAm.)

={c(A,r21A,,,,'2)

whose

it

Hence, although crosstalk does exist, ears become identical when 0=0, namely

in

the in

equation

[ 33

phases at the (:enter

]

to

the left and right Front direction.

Meanwhile

kD

I!l,l

a

b

('\il

iam)(]

!c)cos2_/2

.'(.\ ....

c

kD c tall 2 _/2 kD

',,)

sm2_[;

>1

c tan 21' 2

Therefore, D=i Scm)

(b)

._L).iR

.

If

,

When

ALFe0,

kD x/

2

i,h i,,htI

1 ! (1 707 _ 0 707 tan 0 3 = 1 . (} 7O7 il 707 tan {),3

ARF=O

_

and

0.3

(which

c=_or

is

to

say

30

-3dB: ,\1 p2

From

equation

from which

I 12c

Substituting

c,

[ 33

],

we

have

(l

yeA,,7

'"'%

I_,n,

we

obtain

_ ,, I ,

0u_

t_,_,

or

_2=

21

-

,

:_2_

f

#

300

Hz,

assuming


To find out the velocity potential we again put kD = 0.3, in which case

ratio

between

the

ears,

2v-_

a -Al

. kD , . i.,cos 2 _/_ (cob

k) b =cAivsm2_/2(cos

stn/t)

k) cos]] _/2(cos

, cAl,i

/ I sirv/)_l

64l\1t

o ' _ln//):

027,Mi

Therefore

(c) are

When placed

I_h.I

d

1',5.[

' a--);

b

I 91 --

] 37

[ 39

four microphones having as shown in Fig. V to

Under

that

cosine pick up

is

also

assumed

that

sensitivity input signal':

^,, Aco_(_ .') [ ^., ^.o_(_ .'_ ;

condition,

c

It

directional a 'front

c= il_

_J2

(or

(

/

:id[I)

-3 dB).

Then,

substituting

these

v-f values

in equation

[ 33 ],

we first

obtain

': /'0%1]' S I11It' (1 ' 2c)

into

which

(I ! 2c

[

34

]

2c:)co'¢1/'

we now substitute

c=0.717

to

get

C{3SII'siiiII'

J.:;o7_7o'_¢,,_,.,,,, _......

Again,

based

on the

[

assumption

that

35 ]

Dk

2v--_

= 0.3,

the

directional

angle of the reproduced sound image can be computed from equation [ 35 ]. Fig. IX graphically shows the computed results, and also demonstrates how the directional angle of such a sound image shifts as the amount of crosstalk is controlled. Fig. X extends the foregoing analysis to a complete 360 degrees of directionality, it demonstrates that the matrix system under review locates sound images with complete left-right, frontback symmetry, and also that Jt does not dislocate the Center Front position. It reveals, however that such a matrix tends to shrink the psycho-acoustic distance between the front two speakers and between the rear two.

- 22-


(2) A Matrix System by 90 ° and 180 ° and

in Fig. speakers

Which Phase-Shifts Which Distributes

the the

Such a matrix system provides the XI. The complex volume velocities wi.l] then be I,F RF IAI RB

As before, we first left and right ears [ 4 ] and [ 5 ].

,t_(A_l' 4::(Am ,1= (AL. Izr (A,,

A,,,_ A .... ,\,./

velocity

z2(cob//

..... fi,V_-("'_" .... ,,>, _._,\.... x.,

MnO) I c(All]; kl 2(co_Z_

(\,1

and

,\1

)Mn,i

sm0)

cAll)sm

kI,2

as the

presented four

reaching the Jn formu]as

)

kD

,l!c(At,l_iA.i)t.s,_

> sm,,

potentials abeve values

the

kl) >sin,

output vectors emitted by

I cA.. jCAh,) cAET_ I )cA,n) c\cc t ]CAll) i cA_ i jcAm )

obtain the by substituting

CA....

Rear Channel Signals Crosstalk Asymmetrically.

z2((,os/J

c(/\..

Mp/I) kl) v2(Cc_

Z\ll)C_S

D2(/r),t]-k,

,lIlf/)i(,'\tlt

smU)

LAIn

AE,i

...... /:0

(;c_/!

cai,,)

[ 36 ]

similarly,

,;1_

r

(All

_ '\.,

,'\,1'

c\_l,co_

q

_ 2(rcs

_mU)

_

.Al.i.Ai,i_.i.,:.?/ ........... _.,\.....\.._,.)%, m

) _ Ic(''\ t II

e\]ll)('osZv_(c()sd · kD

sllllll

('(Alii:

A

i)l'()h

_

.. k )2(i,oq//

hlllll )

m

(A,;

,"\ .....

% ......

,\,,

) _,,,:!kl) p

_

( ............

)

_,, ......,,,,,,....... ,,,_,..):%_, ............ _}_ Again, we assume the Left Front

enters

[ 36

]

Since and

a case whore only a 'front and Right Front microphones.

ALB=Ai/B=O, substituting [ 37 ], we have

that

k

jr(l

_/\11

(,zXlt I qlll ' r j_(]

ch\{i

[ z7 ] input

relationship

kI) )[) _tn2, 2

to_

//

kl) 2}_(,o_[/,, hill/I) kI) _lq,

_co%ll

sln'_

\1 %]i1/I,

(L

c).\l..

_'

kl) S 1, _ 2(t_SY (/

()AiH

23

-

NIH;

II :

z

.in//)

Sm/]_ kD kk ()'_[)

%Ill/Y)

signal'

into

equations


For

the

sake

simplicity,

of

we (1

) ,ri

o\

,2(

) ),

All

put

co_,,

c),\.l

/2(_,,_/

Skil//)

_m,2,(cos/}_mfl)

a

b

kD ](1

c;,\

......

j_

2,cos/'

...... )

(I

:c)Aic,

Sln,kl,)z(

.............

)

c

[ c,,\,_ c_ k])2 (co_L'sm//) CALLC_S2_2d) [ , _// , Sin') d Whereupon,

equations

[

'....._ _ i(a

0, 0.

38

] and

]

can

be

,,> j<,.d>';

rewritten

as

[ 40 ]

,J_l'q(a_t>) ' 0(_ <1)}

Consequently, the phase the middle point between

front

[ 39

[ angles of the ears,

41

]

these velocity _I, and _R, are

potentials

d

_' .

Since of the

t""' i, ta. i It' d) a,h

it is our reproduced

,,b

which

We now eventually

[ 4S ]

recall derive

the

k {_, _?,V,,

the

On the ears

abbreviations

sin/l)

other hand, are given by ,.

and

,"A:,. } _,,k,,,,, (_,,.,....... )

5HiI_ 2 [ ..... /

at

(I

'?ÂŁ )'\[ ] '\Ill

the

expand

_'5{0 ,)'\ ....

'111klJ_2

magnitudes

2( ,\1 i Alt[

of

the

,Ix"<" I,, ',, _/"

which

case,

the

"j:

ratio

/ x, ht

}:/

d)

_,t

101,]

b_\

i

, ,t

24

and

d b

;L

kD_ 2 .... //

velocity

{</;Ri is

h

above

equation

'.\,., J

....

[ 48 ]

between

_

the

[ 47 ]

,,;,' ,'\'/_' i,_,<_<1_' in

angle

[ 44l

_,, I,_l

to

]

the directional when _],=_R,

(c d)

,,I,

42

[43]

fundamental assumption that sound 5mage is determined

c d

from

[

[

46

]

potentials


Naturally, b=d=0, so

if

c=0

:!h I 6M

(i.e.,

--_,

crosstalk)

as

in

the

then

if

the

sinx=x. (I

'Jtq(At

J':

sound

source

Equation AI,m'i

2(I

frequency

[ 46

' 2cQAM

Alt[

] can

system,

When ALF=Ap,F and

c=._!_1or xZT

is within

then

be

rewritten

as

trow

EXAMPLES OF COMPUTATIONS FOR THE DIRECTIONAL POTENTIAL RATIO (a)

discrete

1

Furthermore, x/_(_

no

ANGLE 0 AND VELOCITY

-3dB:

Substituting those values in equation [ 50 ] yields from which 0=3SO30 ', so that tho Center Front sound source from a somewhat rightward direction in playback.

-4=tan appears

Assuming ,k_=0. 3, we compute the values of a and b to obtain _v _ Ic)7.\,, and /, o_:_{,,\,, , which we substitute in equation [ 31 ] to obtain the left-to-right velocity potential ratio at the ears: ,t

,h

lb)

When ALF=0,

a

ARF=0 and

b

i <_7 (_ L_6

c=---!_1 or

-3dB:

Substituting the values in equation [ 50 ] gives us which ]n turn gives us 0=90 째 . The Left Front sound source fore appears in the straight leftward direction. Assuming k_=0.3, substituted in equation velocity potential ratio

a=l.63ALF and b=0.209AiF ,,, which are [ 31 ] to determine the left-to-right at the ears: :!;m: ,hi

(c) are of

Following the same computing process as matrix, we eventually obtain from equation 'dLr,_l/'_tlli/'

:It C_)s2//'

2_).,_,,,'

then

O77'

When four microphones having cosine directional placed as shown in Fig. V to pick up a 'front

<B_,,')d

=tan0, there-

(_)_II'slI]I

,,,,,,:,,

sensitivity input signal':

for the [ 33 ]:

I

'

,2

- 25-

' ......

[ S1 ]

first

type

0,


It is evident that the matrix system under review locates sound images asymmetrically, and this fact is clearly disclosed in Fig. XII where the preceding analysis is extended to cover the entire 360 degrees of directionality. Not only does it localize sound images asymmetrically in both left-right and front-back relations, but it mis]ocates the Center Front sound source.

6.

tories) of a source

CONCLUSION An experiment by T. Fujita (NIIK Technical reveals that man's ability to recognize sound source is accurate in ail directions is of a high frequency (see Fig. X]I).

Research Laborathe directionality when the sound

However, for a sound source in the middle and iow frequency range, such ability deteriorates in the front-back direction (i.e., the listener tends to mistake a front source for a back one), yet he is still ab]e to judge the left and right directionalities with accuracy. It was contended in the introduction of this paper (]) that man discerns the directionality of a high-ÂŁrequency sound source on account of the directional sensitivity of his ears, but that he distinguishes that of a low~frequency sound source as a conse-quence of the phase difference his ears perceive. Our theoretical analyses validate such contentions. instance, if two sound sources are located symmetrically -front and back -across the left-right ax]s, the phases of resulting sound waves reachi_lg the left and right ears are so that nlan is unable to distinguish between the front and directional]ties. This is in keeping with the findings of tioned experiment by Fujita (although tl_e frequency ranges in the experiment and in this paper differ somewhat). Thus, we define image, in a four-channel the angle at wbicb the dead center coincide. In the mains unchanged sound field. the inevitable

the

directionality system having phases perceived

a

(2)

For in the the identical, back the men_ considered

of a reproduced sound '2-2' speaker ?os[tien, by a listener sitting in

as the

case

of the discrete system, this directionality reboth in the live sound fie]d and Jn the reproduced This can be said of 4-2--4 matrix systems as well unless crosstalk is phase-shifted.

Once the crosstalk is phase-shifted, however, it becomes im_ possible to reproduce the original sound source directional]ties exactly as they are. Nevertheless, a system that dSstri[mtes the crosstalk symmetrically -- such as the Sansui QS regular matrix system -_ localizes sound images with correct left-right and frontback symmetry. Its drawback is that it tends to shrink the psycheacoustic distance between the Left Front and Right Front speakers, and between the Left Back and Right Back speakers.

26

-


In contrast, asymmetrically and images are located located.

with a system that employs asymmetrically

that distributes the crosstalk asymmetrical phase shifts, sound and therefore tend to be mis-

As for the Sansui QS regular matrix system, the introduction of the Vario-Matrix technique into it permits us to obtain sound image directionalities which are psycho-acoustically equivalent to those of the discrete system. This was demonstrated in Part I of this paper.

27


REFERENCES Part

I

1.

"Proposed Universa] Encoding Standards Channel Matrixing" by R. Itoh (Sansui presented at the 41st Audio Engineering

2.

"The Sansui QS Coding System and a New Technique to Improve its Inter-Channel Separation Characteristic" by R. Itoh and Susumu Takahashi (Sansui Electric Co., Ltd.), presented at the 42nd Audio Engineering Society Convention.

3.

"Temporal Masking of Directional Information" by Masao Ebata, Toshio Sone and Tadamoto Nimura (Tohoku University), Reports of the 1972 Spring Meeting, The Acoustical Society of Japan.

Part

for Compatible FourElectric Co., Ltd.), Society Convention.

II

1.

"Experiments on the Localization Horizontal Plane" by T. Fujita tories), June, 197-.

of Real Sound Sources (NHK Technical Research

2.

"Discrete-Matrix Multichannel Stereo" by D. Cooper (University of Illinois) and T. Shiga (Nippon Columbia Co., Ltd.), Journal of the Audio Engineering Society.

28

in a Labora-


FIG. I.

DIRECTIONALITY OF SOUND SOURCE IN 2-SPEAKER PLAYBACK

Speaker1

Speaker 2

X \

/ X k

/ k

/ X \

/

X

/

/

/

/

/ k

x

x

/

L

¢"

/

/

R

¢'

Speaker 1

Speaker 2

',l/ Speaker i

Speaker 2

...... /

j.

Composite Wave Front \

a. Speakers 1 and 2 Producing Same-Frequency, In-Phase Sounds of Different Levels

,Composite

Wave Front

'

b. Speakers 1 and 2 Producing Same-Frequency, Out-of-Phase Sounds of Same Levels


FIG.

II.

DEFINITION

OF DIRECTIONAL

FIG.

III.

IIOW TO DETERMINE REPRODUCED SOUND

ANGLE

DIRECTIONALITY IMAGE

^ i

i ^n

x,

.1

'

_SL

Vn

t

_"' \.L.,_..ZJ'.D'

5/

Directional

Sensitivity

of Ears

OF


FIG.

IV.

LOCALIZATION O17 A SOUND SOURCE IN '2 - 2' SPEAKER POSITION

Speaker

Speaker

LF

RF

IMAGE

'4 / Speaker

FIG,

V.

I I

/' t D

"_ '%.

I I

_,

Speaker lib

PICK-UP OI,' A SOUND SOURGF, BY F()I, JR MICROPIiONF, S WITI l COSINE DIRECTIONAL SENSITIVITY IN '2 - 2' POSITION

I'

__ Directional

Sensltlmty

SensltlvltV

Directional

Xx.._ j

"x

Y-

Sensitivity

'"%

/ W

FIG.

VI.

1,OCALIZATION ()F A SOUND SOURCii IN4AGE IN '2 - 2' o

_At[_CA_[ *CAin) IF

_ARFI CAL_ CAI_ RF

/r

D

x

,/

"x

/ LB (AL8 ' CALF [ CARII)

____¢____

;

_x REI IA_*B, CAFII _CAtEII


FIG.

VII.

CHANGE INTOTAL ENERGY LF,VEL DUL ? TO CROSSTALK WHEN IDENTICAL SIGNALS EN_FER I.F ANti) RF

rIB 10 9 8 7

g 6 速 E w

5

3 2

0

I

q

-10

--20

_30dB

Crosstalk

FIG.

VIII.

OUTPUT INI}ACH CHANNF, L AS DELIVERED BY A ROTATIONAI,i.Y SYMMWI'RICAL P[IASE-A MPLITUD]'; MATRIX Aaf

t.... CAm _- _

k[_

Acfl

AL_

i" CAt_

CA.s

F_LI

CARU

CALF

Ami


FIG.

IX.

CHANGE IN REPRODUCED DIRECTIONALITY DUE TO CROSSTALK (WHEN USING MICROPI-IONES WIq'H COSINE DIRECTIONAL SENSITIVITY TO FEED IDENrI'ICAL SIGNALS INTO LF AND RF)

_ --20dR

- 3dB

Directional Angle in Live Sound Field

]

-3dB

_45 °

--20dB /

40o. _40 °

// / /

X\

/ \

-co

/ \\

/ / / / /

45 °

40°

30 °

20 °

10°

Directional Angle in Reproduced Sound Field

0

-lO

°

-20 °

-30 °

-40 ° -45 °


FIG.

X,

DIRECTIONAL

CHARACTERISTIC

SYMMETRICAL MICROPHONES

WITH

Directional

COSINE Angle

135"

180'

135 掳

OF

A ROTATIONALLY

PHASE-AMPLITUDE

90 _

45 _ I I I I I I I LF

LB

MATRIX

(WHEN

DIRECTIONAL

in Live Sound

USING

SENSITIVITY)

Field

-135

-45

-90

-135

I Directional

I

in Reproduced

Sound

/

\Xx X

// ./

FIG.

XI.

OUTPUT

RB

IN EACH

CHANNEL

BY AN ASYMMETRICAL :

CALe

CAR_

AS DELIVERED

PHASE

] CAaa

/ CALF

CARt

MATRIX

Air

CALB

b

ARt

RB

CAR_

Field

RB

I RF

LB

-180 I

Angle I RF I I I I I

l

CAL_

ARa


FIG. XII.

DIP,I£CTIONAI, CIIARACTI';RISTICOF AN ASYMMETRICAL PHASE MATRIX (WI I]';N USING MICROPI IONES WIT}t COSINE DIRECTIONA 1, SE NSITIVITY)

Directional

Angle in Live Sound 180 180

135I

180

135 L'B

90

45 I]

III I\\\\ \ \ 'xx. _'" '""" _ i -_LF __ LB

Field

135

90904 45

90

135

'Directional IAngle in Reproduced RB '1

Sound Field,/ 'RF RB

/ / / / // //Ill

180


HG.

XII][.

I)iP,

I'iCTIONAL

(SOUI_.Cb;: T]';CII.

SENSITIVfTY A

1_,1,2S.

RI'POP, f_ABS,

T

BY

OF TAKASIII

HUMAN

EARS

FUJITA,

NI1K

JAPAN)

18o

90 0

i o

250 500Hz 800117 1 6kHz 282 5_63kH ?

9o

DlrectlofXal Arlgle of So_lrld Source

Band Nome

t......... /

18o

Characteristics of the Sansui QS Vario-Matrix 1 and 2  

Part I - CHARACTERISTICS OF THE SANSUI QS VARIO-MATRIX Ryousuke Itoh and Susumu Takahashi Sansui Electric Company Tokyo, Japan 43rd CONVENTI...

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