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
路
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
路
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
路
/ 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