U.S. patent number 3,856,992 [Application Number 05/187,065] was granted by the patent office on 1974-12-24 for multidirectional sound reproduction.
Invention is credited to Duane H. Cooper.
United States Patent |
3,856,992 |
Cooper |
December 24, 1974 |
**Please see images for:
( Certificate of Correction ) ** |
MULTIDIRECTIONAL SOUND REPRODUCTION
Abstract
Multidirectional audio sound signals are encoded in transmission
signals employing phasor matrixing coefficients varying in
amplitude and phase as a continuous function of the bearing angle
or direction of each signal source. The transmission signals are
decoded to provide presentation signals for loudspeaker placement
patterns which may be selected by the listener. Exemplary matrixing
or encoding apparatus and re-matrixing or decoding apparatus are
described.
Inventors: |
Cooper; Duane H. (Champaign,
IL) |
Family
ID: |
22687474 |
Appl.
No.: |
05/187,065 |
Filed: |
October 6, 1971 |
Current U.S.
Class: |
381/23 |
Current CPC
Class: |
H04S
3/02 (20130101) |
Current International
Class: |
H04S
3/00 (20060101); H04S 3/02 (20060101); H04r
005/00 () |
Field of
Search: |
;179/1G,1GQ,15BT,1.4ST,1.41K,1.1TD |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
4 Channels and Compatibility by Scheiber, Audio Engineering Society
Preprint, Oct. 1970. .
Analysing Phase Amplitude Matrices by Scheiber, Audio Engineering
Society Preprint, Oct. 5-8, 1971..
|
Primary Examiner: Claffy; Kathleen H.
Assistant Examiner: D'Amico; Thomas
Attorney, Agent or Firm: Fitch, Even, Tabin &
Luedeka
Claims
What is claimed is:
1. A signal-processing apparatus for use in the production or
reproduction of multidirectional audio signals comprising matrixing
means for producing a set of output signals from a set of input
signals, each signal of at least one of said sets being identified
with a different sound-direction bearing angle, means for mixing
the input signals with mixing coefficients defined for each
respective value of a 360.degree. repetitive single-variable
function of bearing angle for each output signal to provide the
respective output signals, said single-variable functions having
the characteristic that when each output signal is multiplied by
the complex conjugate of the respective function of another bearing
angle and all such products are added, the sum produced thereby is
a sum of input signals each multiplied by a coefficient that is a
function solely of the difference between both bearing angles.
2. A method of reproducing directional audio information from a
plurality of source signals to form a plurality of presentation
signals, comprising the steps of: matrixing source signals
representative of sounds from different bearing angles .theta.,
each measured from a source reference direction, to form
transmission signals having encoding mixing coefficients, at least
one of said transmission signals having encoding mixing
coefficients substantially corresponding to values of a given
single-variable function of the bearing angle .theta. of the
respective sounds, re-matrixing the transmission signals to form
signals for presentation at bearing angles .phi., each measured
from a presentation reference direction having a specific angular
relation to said source reference direction, by multiplying each
transmission signal by a decoding mixing coefficient substantially
corresponding to the vlaue of a single-variable function of .phi.
for each presentation bearing angle, said function of .phi. being
the complex conjugate of the function of .theta. defining the
encoding mixing coefficients for each transmission signal, and
adding the resultant product signals to form each presentation
signal, so that the sum of all products of the function of .theta.
applied to source signals in formation of each transmission signal
with the function of .phi. applied to that transmission signal in
the formation of each presentation signal is a 360.degree.
repetitive single-variable function of the difference between the
angles .theta. and .phi. having a maximum absolute value at a
reference difference angle, a relatively small absolute value at
the diametrically opposite difference angle, and absolute values at
intermediate angles symmetrical with respect to the axis thus
defined.
3. In a method of reproducing directional audio information from a
plurality of source signals to form a plurality of presentation
signals, wherein the source signals are representative of sounds
from different bearing angles .theta., each measured from a source
reference direction, and are matrixed to form transmission signals
having encoding mixing coefficients, at least one of said
transmission signals having encoding mixing coefficients
substantially corresponding to values of a given single-variable
function of the bearing angle .theta. of the respective sounds, the
steps of re-matrixing the transmission signals to form signals for
presentation at bearing angles .phi., each measured from a
presentation reference direction having a specific angular relation
to said source reference direction, by multiplying each
transmission signal by a decoding mixing coefficient substantially
corresponding to the value of a single-variable function of .phi.
for each presentation bearing angle, said function of .phi. being
the complex conjugate of the function of .theta. defining the
encoding mixing coefficients for each transmission signal, and
adding the resultant product signals to form each presentation
signal, so that the sum of all product signals of the function of
.theta. applied to the source signals in formation of each
transmission signal with the function of .phi. applied to that
transmission signal in the formation of each presentation signal is
a 360.degree. repetitive single-variable function of the difference
between the angles .theta. and .phi. having a maximum absolute
value at a reference difference angle, a relatively small absolute
value at the diametrically opposite difference angle, and absolute
values at intermediate angles symmetrical with respect to the axis
thus defined.
4. In a method of producing signals with directional audio
information from a plurality of source signals which includes
matrixing of said source signals representative of sounds from
different bearing angles .theta. to form transmission signals
capable of bein re-matrixed for production of a plurality of
presentation signals at bearing angles .phi., the bearing angles
.theta. being measured from a source reference direction and the
bearing angles .phi. being measured from a presentation reference
direction having a specific angular relation to said source
reference direction, said method comprising the steps of mixing the
source signals with mixing coefficients defined for each respective
value of a given 360.degree. repetitive single-variable function of
the bearing angles .theta. for each transmission signal to provide
said transmission signals, the respective single-variable functions
having the characteristic that when each transmission signal is
multiplied by the complex conjugate of the respective function of
the bearing angle .phi. and all such products are added, the sum
produced thereby is a sum of input signals each multiplied by a
coefficient that is a function solely of the difference between
said bearing angles .theta. and .phi., and has a maximum absolute
value at a reference difference angle, a relatively small absolute
value at the diametrically opposite difference angle and absolute
values at intermediate angles symmetrical with the respect to the
axis thus defined.
5. An audio recording having transmission signals formed from the
matrixing of a plurality of source signals representative of sounds
from different bearing angles .theta. and capable of being
re-matrixed for production of a plurality of presentation signals
at bearing angles .phi., the bearing angles .theta. being measured
from a source reference direction and the bearing angles .phi.
being measured from a presentation refererence direction having a
specific angular relation to said source reference direction, at
least one of said transmission signals including the sum of mixed
signals each formed by mixing the source signals with mixing
coefficients defined for each respective value of a given
360.degree. repetitive single-variable function of the bearing
angles .theta. for each transmission signal, and said given
single-variable function has the characteristic that when it is
multiplied by the complex conjugate of said function of the bearing
angle .phi. and all such product functions are added, the sum
produced thereby is a function solely of the difference between
said bearing angles .theta. and .phi., and has a maximum absolute
value at a reference difference angle, a relatively small absolute
value at the diametrically opposite difference angle and absolute
values at intermediate angles symmetrical with respect to the axis
thus defined.
6. In the method of reproducing directional audio information which
includes producing source signals corresponding to sound emanating
from locations at bearing angles differing in side-to-side and
front-to-back orientation with respect to a listener, the steps of
encoding and mixing the source signals in accordance with first
sets of predetermined amplitude and phase coefficients said first
sets of coefficients being defined by 360.degree. repetitive
functions of said source bearing angles to produce a number of
transmission signals smaller than the number of source signals,
there being a respective function for each transmission signal, and
decoding and separating the transmission signals in accordance with
second sets of predetermined amplitude and phase coefficients said
second sets of coefficients being defined by complex conjugates of
said respective functions of a presentation bearing angle to
produce presentation signals corresponding to angular positions of
greater number than the number of transmission signals, each
presentation signal comprising a plurality of source signals mixed
in accordance with third sets of amplitude and phase coefficients
constituting sums of products of said first and second sets, the
coefficients of the third sets representing the proportion with
which each source signal component is represented in each
presentation signal, said coefficients of said third set being
defined by functions of the bearing angles between the source
direction and the presentation direction and all of said functions
being identical for all such third set coefficients, whereby the
presentation signals are directionally symmetrical.
7. A signal-processing system for producing or reproducing
directional audio information comprising encoding means for
matrixing source signals representative of sounds from different
bearing angles .theta., each measured from a source reference
direction, to form transmission signals having encoding mixing
coefficients, at least one of said signals having encoding mixing
coefficients substantially corresponding to values of a given
single-variable function of the bearing angle .theta. of the
respective sounds, decoding means for re-matrixing the transmission
signals to form signals for presentation at bearing angles .phi.,
each measured from a presentation reference direction having a
specific angular relation to said source reference direction, said
decoding means having means for multiplying each transmission
signal by a decoding mixing coefficient substantially corresponding
to the value of a single-variable function of .phi. for each
presentation bearing angle, said function of .phi. being the
complex conjugate of the function of .theta. defining the encoding
mixing coefficients for each transmission signal, and means for
adding the resultant product signals to form each presentation
signal, so that the sum of all products of the function of .theta.
applied to the source signals in formation of each transmission
signal with the function of .phi. applied to that transmission
signal in the formation of each presentation signal is a
360.degree. repetitive single-variable function of the difference
between the angles .theta. and .phi. having a maximum absolute
value at a reference difference angle, a relatively small absolute
value at the diametrically opposite difference angle, and absolute
values at intermediate angles symmetrical with respect to the axis
thus defined.
8. In a signal-processing apparatus for reproducing directional
audio information from a plurality of source signals to form a
plurality of presentation signals, wherein the source signals are
representative of sounds from different bearing angles .theta.,
each measured from a source reference direction, to form
transmission signals having encoding mixing coefficients, at least
one of said signals having encoding mixing coefficients
substantially corresponding to values of a given single-variable
function of the bearing angle .theta. of the respective sounds,
said apparatus comprising decoding means for re-matrixing the
transmission signals to form signals for presentation at bearing
angles .phi., each measured from a presentation reference direction
having a specific angular relation to said source reference
direction, said decoding means having means for multiplying each
transmission signal by a decoding mixing coefficient substantially
corresponding to the value of a single-variable function of .phi.
for each presentation bearing angle, said function of .phi. being
the complex conjugate of the function of .theta. defining the
encoding mixing coefficients for each transmission signal, and
means for adding the resultant product signals to form each
presentation signal, so that the sum of all products of the
function of .theta. applied to the source signals in formation of
each transmission signal with the function of .phi. applied to that
transmission signal in the formation of each presentation signal is
a 360.degree. repetitive single-variable function of the difference
between the angles .theta. and .phi. having a maximum absolute
value at a reference difference angle, a relatively small absolute
value at the diametrically opposite difference angle, and absolute
values at intermediate angles symmetrical with respect to the axis
thus defined.
9. The method of claim 4 for producing two transmission signals
wherein the transmission signals are formed as one of the following
pairs: ##SPC9##
where S.sub.k is the k-th source signal, .theta..sub.k is the
bearing angle between the sound location thereby represented and a
laterally central reference location and j is the square root of
-1.
10. The method of claim 3 for producing presentation signals from
two transmission signals T.sub.L and T.sub.R wherein each
presentation signal P.sub.i is formed from the transmission signals
by mixing thereof in the amplitude and phase relation
P.sub.i = T.sub.L [1 + e.sup..sup.-j (.sup..phi. .sup.+
.sup..pi./2) )] + T.sub.R [1 - e.sup..sup.-j (.sup..phi. .sup.+
.sup..pi./2) ]
where .phi..sub.i is the bearing angle between a presentation
location i and a laterally central reference location and j is the
square root of -1.
11. The improved method of claim 6 wherein said function is
proportional to the quantity 1 + e.sup.j.sup..alpha. , where
.alpha. is the angle between the source direction and the
presentation direction and j is the square root of -1.
12. The improved method of claim 6 for stereo-compatible and
mono-compatible reproduction wherein there are two transmission
signals T.sub.L and T.sub.R formed from n source signals
substantially as follows: ##SPC10##
where S.sub.k is the k-th source signal, .theta..sub.k is the
bearing angle between the sound location thereby represented and a
laterally central reference location and j is the square root of
-1.
13. The improved method of claim 6 for stereo-compatible and
mono-compatible reproduction wherein there are two transmission
signals T.sub..SIGMA. and T.sub..delta. formed from n source
signals substantially as follows: ##SPC11##
where S.sub.k is the k-th source signal, .theta..sub.k is the
bearing angle between the sound location thereby represented and a
laterally central reference location and j is the square root of
-1.
14. The method of claim 6 for reproduction of four source signals
corresponding to mutually orthogonal sound locations by
presentation to a listener from these same mutually orthogonal
locations wherein each presentation signal contains the
corresponding-location source signal plus each of the
adjacent-location source signals, both of the latter being reduced
to 0.707 in relative amplitude, and one of them being advanced in
relative phase by 45.degree. and the other being retarded in
relative phase by 45.degree., with respect to the corresponding
location signal.
15. The method of claim 11 wherein the sound locations are at left,
front, right and back, the corresponding source signals being
S.sub.L, S.sub.F, S.sub.R and S.sub.B, and the corresponding
presentation signals being P.sub.L, P.sub.F, P.sub.R and P.sub.B,
respectively, and the transmission signals being T.sub.L and
T.sub.R, the first sets of coefficients being:
T.sub.L = S.sub.L + 0.707 S.sub.F +45.degree. + 0.707 S.sub.B
-45.degree.
T.sub.R = S.sub.R + 0.707 S.sub.F -45.degree. + 0.707 S.sub.B
+45.degree.
and the second sets of coefficients being:
P.sub.L = T.sub.L 0.degree.
P.sub.F = 0.707 T.sub.L -45.degree. + 0.707 T.sub.R +45.degree.
P.sub.R = T.sub.R 0.degree.
P.sub.B = 0.707 T.sub.L +45.degree. + 0.707 T.sub.R -45.degree.
16. The method of claim 14 wherein the sound locations are at left
front, right front, right back and left back, the corresponding
source signals being S.sub.LF, S.sub.RF, S.sub.RB and S.sub.LB, and
the corresponding presentation signals being P.sub.LF, P.sub.RF,
P.sub.RB and P.sub.LB, respectively, and the transmission signals
being T.sub.L and T.sub.R, the first sets of coefficients
being:
T.sub.L = 0.924 S.sub.LF +221/2.degree. + 0.383 S.sub.RF
+671/2.degree.
+ 0.383 S.sub.RB -671/2.degree. + 0.924 S.sub.LB -221/2.degree.
T.sub.R = 0.383 S.sub.LF -671/2.degree. + 0.924 S.sub.RF
-221/2.degree.
+ 0.924 S.sub.RB +221/2.degree. + 0.383 S.sub.LB +671/2.degree.
and the second sets of coefficients being:
P.sub.LF = 0.924 T.sub.L -221/2.degree. + 0.383 T.sub.R
+671/2.degree.
P.sub.RF = 0.383 T.sub.L -671/2.degree. + 0.924 T.sub.R
+221/2.degree.
P.sub.RB = 0.383 T.sub.L +671/2.degree. + 0.924 T.sub.R
-221/2.degree.
P.sub.LB = 0.924 T.sub.L +221/2.degree. + 0.383 T.sub.R
-671/2.degree.
17. The signal-processing apparatus of claim 1 comprising an
encoder having input sound-source signals of various bearing angles
and output transmission signals.
Description
This invention relates to reproduction of multidirectional audio
program material with greater directionality and ambience than
those of conventional stereo reproduction, and to the recording
and/or transmission of program material for such reproduction. More
particularly, the invention relates to the coding or mixing of
directional sound information into a number of recording or
transmission channels smaller (at least normally) than the number
of sound sources to be reproduced and decoding or signal treatment
and distribution of the content of these channels to reproducers
differing in number or location from the sound-source locations for
reproduction simulating presence at the original performance in
psychoacoustic impression.
Although the invention in its broader aspects is not limited to any
specific number of sound sources (typified by microphones) or
reproducers (typically loudspeakers), it will most readily be
understood by initial reference to the type of reproduction which
has become popularly known as "quadrasonic" or "quad," an extension
of two-speaker stereo techniques to the reproduction of
multidirectional program material with four loudspeakers to
increase the sensory illusion of presence or ambience. The term
"quadrasonic" originated to describe systems wherein exciting or
presentation signals for individual reproducers are maintained in
separate and discrete form as separate signal channels, as in
four-speaker reproduction from four-track tape. However the term is
now commonly used, and is used herein, to include what have
sometimes been called "pseudo" four-channel systems, wherein four
(or more) original directional sound-source channels are mixed or
combined by encoding into two signal channels, and thereafter
decoded to produce four presentation signals for feeding the
speakers. It is impossible, in such a manner, to produce exact or
pure correspondence between the excitation of each loudspeaker and
the output of a correspondingly located microphone. But it has been
known for some time that results which are psychoacoustically
reasonably simulative of transmission through four discrete
channels can be obtained by such "4 to 2 to 4" signal processing or
matrixing. (There also exist systems wherein no directional
information whatever is added to conventional stereo signals, the
latter being processes, with preselected delay, etc., to feed one
or more back speakers in addition to the conventional front
speakers, thus producing wholly synthetic psychoacoustic
impressions of added directional effects, but the present invention
is not directly concerned with these.)
A present requirement for widespread adoption of any quadrasonic
system is that of compatibility with continued use of existing
reproducing equipment, monaural and stereo. Stated otherwise, it is
generally recognized that recordings made for quadrasonic
reproduction are desirably capable of satisfactory reproduction by
monaural record-players and conventional stereo record-players, and
quadrasonic FM transmissions (whether live or from recordings) must
similarly be reproduced as monaural or stereo material by existing
receivers.
A number of encoding and decoding systems compatible with mono and
stereo equipment have been proposed, and some have been the subject
of experimentation and preliminary forms of commercialization. A
recent publication on the subject is the paper of Peter Scheiber in
Journal of the Audio Engineering Socity, Volume 19, page 267
(April, 1971) describing such a system. A number of other systems
have been devised by or for various producers of phonograph
records, signal-processing equipment, etc. All of these are found
on analysis to have various drawbacks or objections. The relative
importance of the weaknesses or inadequacies of each of such known
systems is differently estimated by their proponents, but none of
the 4-2-4 systems heretofore proposed has been sufficiently close
to the performance of discrete four-channel reproduction to result
in adoption as a standard system of encoding and decoding for use
in stereo disc recordings and stereo FM broadcasting equipment.
The present invention flows from study of the weaknesses or
inadequacies of the systems heretofore proposed, and lies in the
devising of novel methods and apparatus of encoding and decoding
multiple-source and multiple-reproducer signals which not only
involve a minimum of sacrifice of the performance obtained with the
respective reproducer signals maintained in separate channels
throughout, but additionally provide much greater flexibility than
previous systems afford.
Full details of the fairly numerous two-channel matrixing systems
recently proposed or introduced by the record and equipment
manufacturers mentioned above do not appear to be publicly
available, but the general nature of their imperfections in
performance are observable. In any such system, including the
present system, a sound which emanates from a single point (notably
a point located to activate only a single microphone) is ultimately
reproduced not from a single loudspeaker, but from a plurality of
differently located loudspeakers, excited from the same original
source but with an excitation amplitude relation such that from a
psychoacoustic standpoint reproduction from a single direction is
satisfactorily simulated. However, in the systems heretofore
devised, the satisfactoriness of this illusion of directionality is
not uniform for all directions. The nature of the anomalies or
directional ambiquities in signals intended to appear to the
listener to come from particular directions in the prior art
systems is not wholly identical in each case, nor are the sound
directions from which the prior art matrixing systems produce such
anomalous results the same. Typical examples, however, are
opposite-phase reproduction from rear speakers and similar
anomalies which result in more faithful reproduction of
front-oriented sounds than rear-oriented sounds. In some cases, the
anomalies are more or less negligible in psychoacoustic impression
with most program materials, but become highly noticeable with
materials with "sound effects" specifically designed for
quadrasonic reproduction, wherein rear sounds are not merely
supplementary.
It is the principal object of the present invention to provide an
encoding and decoding system for quadrasonic or similar reproducing
systems which avoids such flaws or imperfections of previous
systems, and thus more closely approaches the psychoacoustic
simulation of systems employing completely separate and discrete
signal channels for the excitation of each reproducer. In addition
to achieving this principal object, however, the invention provides
methods and apparatus whereby it is unnecessary to maintain, for
satisfactory performance, a single predetermined set of positions
of the loudspeakers with respect to the listener to produce
satisfactory reproduction. The systems of the prior art (including
transmission in four discrete channels) require a single specific
orientation of the loudspeakers with respect to the listener. In
most cases, a pair of back speakers is added to the front speakers
of a conventional stereo system to form a "2 plus 2" array. In at
least one case, however, the speakers are to be arranged in the
form of a diamond or "1-2-1" i.e., at opposite sides of the
listener and at the center front and back. With all these prior art
systems, the required speaker orientation is specified in
connection with the directions represented by the four discrete
transmission channels or with the coding used in the two-channel
transmission or recording, and no manner is provided, so far as is
known, for using different speaker orientations, or a different
number of speakers, while retaining satisfactory reproduction.
Unlike the encoding and decoding systems of the prior art, the
encoding and decoding of the present invention is capable of
producing the same reproduction characteristics for all directions,
and may be described as "directionally symmetrical." The meaning of
this term as herein used may be most easily understood by
considering the simple example of the reproduction of a sound whose
source is successively moved to actuate each of four orthogonally
located microphones in succession. In a system with directional
symmetry, a listener who turns through corresponding successive
90.degree. angles hears the sound source in wholly identical
fashion as it is correspondingly moved through the four positions.
This property is inherent in a quadrasonic system with a separate
signal channel for transmission of each microphone output but is
not obtainable with prior art "4-2-4" matrix systems. As indicated
above, this is particularly important in permitting use of new
types of program material wherein there is to be conveyed a
realistic impression of an independent sound source (a voice or
chorus for example) at a localized location rearward of the
listener.
In addition to eliminating this limitation on utility, the
directional symmetry of the matrixing, as a further aspect of the
invention, permits simple signal-conversion whereby the geometry of
a loudspeaker system may be "rotated" with respect to the
loudspeaker geometry assumed in the signal-production to permit
wholly satisfactory reproduction of (for example) a recording or FM
transmission designed for "2-plus-2" speaker orientation by a
reproducing system with speakers arranged in the "1-2-1" form of a
diamond, or vice versa. Indeed, the invention provides methods and
apparatus whereby the number and arrangement of speakers to be used
in reproduction is essentially unidentified in the signal
transmission, which is "universal" and may be decoded into
presentation signals for feeding any desired number and orientation
of speakers. The two encoded transmission channels may be decoded
to produce, for example, six speaker-feed signals, with the
speakers disposed in the form of a hexagon, the resultant listener
sensation approximating that obtained with discrete six-channel
transmission. As will later appear, the principles of the invention
may also be employed to provide analogous flexibility in
reproduction of signals transmitted in more than two channels.
The invention accordingly provides decoders producing readily
selectable presentation signals for the number and pattern of the
array of loudspeakers preferred by the listener, as well as
equipment whereby encoding of multi-directional sound into a
plurality of channels, and selection of directional effects, may be
simply performed by a recording studio or record manufacturer or
broadcaster without limitation to expected use by only those
listeners having a specific loudspeaker arrangement.
The universal or rotatable aspect of the relation between encoding
and decoding of the transmission signals of the invention is
obtained by the employment of mixing coefficients which alter both
the phase and amplitude of each source signal, in encoding, and of
each transmission signal, in decoding, in a manner producing an
overall reproduction matrix wherein the phase and amplitude of
appearance of any source-signal in any presentation signal is
entirely a function of the angular relation between the azimuthal
location of the source and the azimuthal location of the speaker
for which the presentation signal is formed, i.e., of the
difference in bearing angles of the source and the reproducing
loudspeaker.
The invention will be best understood by referring to the
explanatory illustrations and embodiments of the invention in the
attached drawing, in which:
FIG. 1 is a schematic illustration of one type of quadrasonic sound
reproduction system;
FIG. 2 is a similar illustration of a variant type of quadrasonic
sound reproduction system;
FIG. 3 is a similar illustration, but differing from the previous
Figures in the employment of non-corresponding source-signal and
reproduction locations;
FIG. 4 is a schematic view illustrating certain angular relations
employed in the invention;
FIG. 5 shows phasor diagrams of transmission signals formed in
accordance with the invention;
FIG. 6 is a block diagram of an exemplary single-signal encoder
embodying the invention;
FIG. 7 is a block diagram of a "universal" encoder for numerous
sound signals embodying the invention;
FIG. 8 is a block diagram of one form of decoder incorporating the
invention;
FIG. 9 is a block diagram of another form of decoder of the
invention; and
FIG. 10 is a block diagram of an adapter circuit for employing the
decoder of FIG. 9 with conventional stereo signals.
In FIGS. 1 through 3 there are shown basic forms of quadrasonic
sound systems which may advantageously employ the invention. FIGS.
1 and 2 show systems which are, except for the matrices for
encoding and decoding transmission signals, the same as certain
systems of the prior art. These exemplary systems are illustrated
and described to facilitate understanding of the advantages and
broad utility of the encoding and decoding (alternatively called
matrixing and re-matrixing) of the present invention to be later
described.
The systems of FIGS. 1 and 2 are alternate forms of quadrasonic
systems heretofore employed with various matrixing systems. In each
case, there is shown an array or pattern of orthogonal microphones
20 or 20a at a program location with a corresponding orthogonal
array or pattern of loudspeakers 22 or 22a in the listening space
surrounding a listener 23. In the system of FIG. 2, the microphones
20a are arranged to receive sounds from, and the speakers 22a are
arranged to reproduce sounds from, locations at the left front
(LF), right front (RF), right back (RB), and left back (LB)
portions of the program and listening spaces, respectively, while
in FIG. 1 the locations 20 and 22 are at front (F), right (R), back
(B) and left (L).
Encoders or matrixers 24 and 24a produce two transmission signals
at 26 or 26a which are then decoded or rematrixed at 28 or 28a to
produce presentation signals for driving the speakers at the
corresponding locations.
Although the representations of speaker locations at LR, LF, LB and
RB in FIG. 2 and at L, F, R and B in FIG. 1 are more or less truly
representative of locations actually used in practice in what are
called "2-plus-2" and "1-2-1" quadrasonic orientations, the
corresponding showings of the microphones will be recognized by
those skilled in the art as considerably simplified showings of
actual microphone placements normally used for quadrasonic
reproduction, particularly in making recordings. Although simple
systems such as illustrated, i.e., four directional
(cardioid-pattern) microphones, can be and are sometimes used, for
example at a normal listener location in a concert hall, it is more
common to employ more complex microphone arrangements and to blend
the outputs of various microphones for effects judged most
pleasing; indeed, as in the case of ordinary stereo
recording-studio and broadcast-studio techniques, the
multidirectional signals may be synthesized or assembled from a
much larger number of sound tracks of individual instruments or
groups of instruments. It will accordingly be understood, both in
connection with the drawing and in connection with further
discussion herein, that an audio signal representative of the sound
from a particular direction may be wholly synthetic as regards
directional information. As later seen, the present invention
additionally provides simple means for such synthesis.
As will also be understood by those skilled in the art, the
illustrations of FIGS. 1 and 2 represent signal-formation and
processing operations which may be carried out in a manner
producing instantaneous reproduction of live program material but
more normally involve some form of storage, i.e., recording, of the
signals at one or more points in the sequence. Typically, the two
transmission signals are the "left" and "right" groove-walls of an
ordinary disc recording or the corresponding audio channels of a
stereo broadcast; it is of course the two-channel limits presently
imposed by these media which creates the greatest necessity for
encoding and decoding, rather than direct transmission in discrete
channels.
The matrixing or coding of the present invention is advantageously
employed in even a simple fixed-position system such as that of
FIG. 1 or FIG 2 because of the directional symmetry which the
invention affords. However, a further advantage of the present
matrixing method and apparatus is its breadth of utility. The
present matrixing is not only readily adapted to use in the systems
of both FIGS. 1 and 2, but permits decoding for highly satisfactory
use of loudspeaker geometries or orientations which are not in any
way "matched" to the source-signal geometry or orientation. One
example of such an overall system is shown in FIG. 3, where outputs
of the microphone system (or synthesized directional signals
representative of sound sources) 20a and encoder 24a of FIG. 2 are
reproduced by the decoder 28 and loudspeakers 22 of FIG. 2. As will
be seen below, the present matrixing or coding and decoding system
not only gives excellent reproduction from all angles with such
"rotated" geometries but permits employment of even more diverse
source-signal and reproduction geometries, such as the employment
of any number of loudspeakers desired by the listener.
FIG. 4 illustrates, for identification, certain angular relations
employed in the matrixing and re-matrixing or coding and decoding
of the invention. In the present invention, the magnitude and phase
with which each source signal appears in each presentation signal
is determined wholly and solely by the angular relation between the
direction or location represented by the source signal and the
direction or location of the loudspeaker to which the presentation
signal is to be fed. Where the overall reproduction matrix (the
product of the encoding and decoding matrices) is such that the
magnitude and phase of each source signal (relative to its original
magnitude and phase) in each presentation signal is everywhere a
function of only this angular relation, complete directional
symmetry is achieved in any system like that of FIGS. 1 to 3. The
angle between any given sound source (actual or synthesized
microphone placement) and loudspeaker location may be designated as
.alpha., shown in FIG. 4. It will be seen that all values of
.alpha. are the same in FIG. 1 and FIG. 2, and identical overall
matrices for both of these geometries are accordingly produced by
the invention, as later seen. However, the encoding matrices at 24
and 24a in the respective Figures are not numerically the same but
are desirably selected in a manner preserving stereo compatibility,
i.e., capability of stereo reproduction on equipment having no
decoder. This is done, as hereinafter amplified, by determining the
encoding matrix coefficients at 24 or 24a in accordance with an
angle .theta. defining the bearing angle of each source with
respect to a laterally neutral (front or back) direction and
determining the matrix coefficients of the decoder 28 or 28a in
accordance with the bearing angle .phi. of each loudspeaker with
respect to a laterally neutral position in forming the presentation
angle .phi. of each loudspeaker with respect to a laterally neutral
position in forming the presentation signals. As shown in FIG. 4,
and as adopted in the further description of the invention, the
laterally neutral reference position is considered the front
position and angles are measured clockwise; but reference herein to
"left," "right," and similar terminology will be understood to be
used for convenience of expression rather than specific limitation,
the effects of reversals, etc., being obvious.
As will be obvious, no matrixing and re-matrixing can produce an
overall matrix which is "perfect" in the same sense as perfection
can be obtained where there is no necessity of compressing the
number of signal channels for transmission. However the
requirements of a perfect overall matrix are mor closely met than
heretofore known by employing matrices of the present
invention.
A "universal" encoding matrix for forming two transmission signals
T.sub.L and T.sub.R from any number, n, of sources is: ##SPC1##
where S.sub.k is the k-th source signal, .theta..sub.k is the
bearing angle between the sound location thereby represented and a
laterally central reference location and j is the square root of
-1.
It will of course be understood that the equality symbol
hereinafter refers to proportionality, uniform changes in absolute
magnitude in signal-processing being irrelevant.
The phasor coefficients of the respective transmission signals
T.sub.L and T.sub.R are shown in FIG. 5 for the particular source
positions previously discussed. Signals from (i.e., to appear to be
"from" upon reproduction) the left, L, are reproduced in the full
amplitude and original phase in the T.sub.L signal, but are zero in
the T.sub.R signal, and vice versa. The signals from other bearing
angles appear in both transmission signals but always in quadrature
phase relation, one leading and one lagging the reference phase,
which is preserved in the L and R signals. The magnitude of each
component is diminished with increase of its relative phase angle
(positive or negative), reaching zero at each 90.degree. phase
angle (180.degree. difference in source location). The mixing
equations below, calculated from the "universal" matrix above, may
be employed for utilizing the invention with fixed four-microphone
placements, with or without the addition of other signals such as
the "on-mic" touch-up signals frequently added for solosits and
other special effects. For the 1-2-1 source orientation, numerical
values of the mixing equations are:
T.sub.L = S.sub.L + 0.707 S.sub.F +45.degree. + 0.707 S.sub.B
-45.degree.
T.sub.R = S.sub.R + 0.707 S.sub.F -45.degree. + 0.707 S.sub.B
+45.degree.
For the 2-plus-2 source orientation, numerical values of the mixing
equations are:
T.sub.L = 0.924 S.sub.LF +221/2.degree. + 0.383 S.sub.RF +
671/2.degree. + 0.383 S.sub.RB -671/2.degree. + 0.924 S.sub.LB
-221/2.degree.
T.sub.R = 0.383 S.sub.LF -671/2.degree. + 0.924 S.sub.RF
-221/2.degree. + 0.924 S.sub.RB +221/2.degree. + 0.383 S.sub.LB
+671/2.degree.
Fixed circuits for producing the desired mixing for one or both
these fixed microphone placements may be constructed if so desired,
with or without employment of microphone directional patterns.
Additional insertion of signal material may then be made to
simulate performance at any location by employment of additional
mixers such as shown in the schematic diagram of FIG. 6.
As shown in FIG. 6, the input signal S is fed to a 90.degree. phase
splitter 30 which produces a positive and a negative
reference-phase signal and a positive and a negative 90.degree.
phase-shifted signal. The reference signals and the phase-shifted
signals are attenuated (and reversed in polarity where appropriate)
in sine and cosine potentiometers 32 and 34 set to the bearing
angle at which the signal S is to be simulatively inserted. The
positive reference signal and the potentiometer outputs are mixed
in summers 36 and 38, the outputs of which are then inserted as
components of the signals T.sub.L and T.sub.R, respectively, in
accordance with the basic encoding equations earlier stated.
In principle, a mixer such as shown in FIG. 6 may be employed for
each sound-source direction. However where a substantial number of
microphones or sound-tracks are desired to be recorded or broadcast
in readily selectable angular positions, the number of phase
shifters required may be greatly reduced by employing a
construction such as shown in FIG. 7. As there shown, each of the
signals S.sub.1, S.sub.2, etc. is fed to a polarity splitter (phase
inverter) 40. The positive or in-phase and negative or
opposite-phase signal are fed to a sine-cosine potentiometer
producing positive and negative signals of amplitude and polarity
determined by the angle of potentiometer setting. The unattenuated
positive signals and the negative sine signals (which are of course
in positive phase for angles having negative sine values) from all
sources are mixed in a summer 44. The positive cosine-amplitude
signals (negative in phase for angles having negative cosine
values) are mixed in a summer 46. The output of the latter is
advanced in phase by 90.degree. at 48 with respect to the output of
the summer 44 and the two are mixed or summed at 50 to form the
signal T.sub.L. (As will be recognized by those skilled in the art,
the output of the summer 44 must be fed to the summer 50 through a
reference-phase portion 52 of the phase shifter 48, the phase-shift
of presently available frequency-independent phase-shifters being
the difference in phase between the phase-shifted output and the
output of a reference-phase channel such as shown at 52, rather
than the phase difference between output and input.)
In similar fashion, the positive input signals and the positive
sine-function signals from all sources are mixed in a summer 54 and
the negative cosine function signals in a summer 56. The latter
summed output is advanced in phase by 90.degree. at 58 relative to
the reference phase 60 of the output of summer 54, and these are
likewise summed at 62 to form the transmission signal T.sub.R.
Persons skilled in the art will immediately recognize that the
functions performed by certain of the elements shown in FIG. 7 as
circuit elements may be carried out by employment of other
techniques which are well-known as equivalents for performing such
functions in recording and broadcast practice. For example,
microphone sensitivity patterns of well-known types may readily be
employed in substitution for the indicated attenuation
potentiometer networks of some or all of the signals S.sub.1,
S.sub.2, etc., in the signal-mixing system of FIG. 7. Orthogonally
positioned dipole microphones may be employed to produce directly
the signals attenuated in accordance with the sine and cosine of
the azimuthal angle of the incident sound sources, with a closely
adjacent single omnidirectional microphone employed to produce the
unity or unattenuated components.
As earlier indicated, the transmission signals T.sub.L and T.sub.R
may either be recorded on any conventional medium, notably a stereo
disc or tape recording, or used for instantaneous reproduction, as
in quadrasonic FM broadcasting employing the two audio channels
provided for ordinary stereo.
The manner of decoding of the signals of FIG. 5 may now be
considered. The decoding closely resembles the encoding, except
that the coefficients applied to the transmission signals in the
forming of each presentation signal are functions of the angle
.phi., the listening-space bearing-angle of the loudspeaker for
which each presentation signal is formed. Each presentation signal
P.sub.i is formed from the transmission signals by mixing in the
amplitude and phase relation
P.sub.i = T.sub.L [1 + e.sup..sup.-j(.sup..phi.i .sup.+ .sup..pi.
/2) ] + T.sub.R [1 - e.sup..sup.-j(.sup..phi.i .sup.+ .sup..pi./2)
] =
T.sub.L (1-sin .phi..sub.i - j(cos .phi..sub.i) + T.sub.R (1 + sin
.phi..sub.i + j cos .phi..sub.i) (2)
where .phi..sub.i is the bearing angle between the presentation
location and a laterally central reference location and j is the
square root of -1. Thus each presenation signal is formed by
multiplying each transmission signal by the complex conjugate of
the multiplier or coefficient used (or which would have been used)
in inserting signal from that bearing angle in forming the
transmission signal, and the resulting respective products are then
added. Each resultant presentation signal P.sub.i is thus:
##SPC2##
The presentation signal P.sub.L for a speaker at the left position
is thus the signal T.sub.L as illustrated in FIG. 5, unaltered, and
T.sub.R is likewise presented unaltered in forming a presentation
signal for a speaker at R (if there is one). Presentation signals
for other positions are exactly the same in appearance of phasor
diagrams, except that the locations represented are intermediate
between the 180.degree. relation shown in FIG. 5 for the L and R
signals. Except for a source signal diametrically opposite the
presentation point, all source signals appear in every presentation
signal, but with a magnitude which varies continuously from maximum
to zero as a function of magnitude of the angle between the signal
source direction and the presentation direction.
For the 1-2-1 speaker orientation, numerical values of the decoding
equation (2) are:
P.sub.L = T.sub.L .angle.0.degree.
P.sub.F = 0.707 T.sub.L .angle.-45.degree. + 0.707 T.sub.R
.angle.+45.degree.
P.sub.R = T.sub.R .angle.0.degree.
P.sub.B = 0.707 T.sub.L .angle.+45.degree. + 0.707 T.sub.R
.angle.-45.degree.
For the 2-plus-2 speaker orientation, numerical values of the
decoding equation (2) are:
P.sub.LF = 0.924 T.sub.L .angle.-22 1/2.degree. + 0.383 T.sub.R
.angle.+671/2.degree.
P.sub.RF = 0.383 T.sub.L .angle.-671/2.degree. + 0.924 T.sub.R
.angle.+221/2.degree.
P.sub.RB = 0.383 T.sub.L .angle.+671/2.degree. + 0.924 T.sub.R
.angle.-221/2.degree.
P.sub.LB = 0.924 T.sub.L .angle.+221/2.degree. + 0.383 T.sub.R
.angle.-671/2.degree.
It may be noted that the overall transmission or reproduction is
not affected by the choice of transmission signals T.sub.L and
T.sub.R to correspond to left and right directions, identical
results being obtained with any choice of diametrically opposed
directions for transmission in original phase and amplitude in the
two respective channels. Association of the transmission signals
with the left and right directions, however, provides compatibility
with ordinary stereo equipment.
Playback equipment permitting selection of an individual speaker
location at any desired angle whatever may be devised along the
same lines as the signal-preparation equipment earlier described.
However such provision is in general superfluous, since practical
speaker placements are not nearly as diverse as microphone
placements, in which balance as between front and back, right and
left, etc., is optional rather than a requirement. The fixed
presentation-signal outputs for the eight positions illustrated
suffice to cover the needs and preferences of users of
four-speakers systems, while intervals of 15.degree. are wholly
adequate for virtually any practical use.
There is shown in FIG. 8 one construction for a decoder which may
be employed with a very wide variety of speaker geometries. The
respective transmission signals T.sub.L and T.sub.R are fed to
90.degree. phase shifters 70 and 72, each of which has positive and
negative reference-phase and phase-shifted outputs. These outputs
are fed to a fixed mixing network 74 consisting of voltage-dividers
attenuating the input signals and distributing the signals so
attenuated to summers producing outputs in accordance with equation
(2). Fixed output terminals 76 are provided for presentation
through suitable amplifiers by loudspeakers at any selected
multiple of 15.degree. intervals (or any other intervals for which
outputs are provided). The number of placement of speakers may thus
be selected in accordance with the preference (including economic
limitations) of the user. In general, the speakers are normally
preferred to be equally spaced in bearing-angle and equidistant
from the listening position, i.e., disposed in the form of a square
or regular polygon. However room shape and acoustics and personal
preferences may result in other arrangements in many cases.
Another form of decoder with selectable fixed-location output
terminals is shown in FIG. 9. The transmission signals T.sub.L and
T.sub.R are fed to a sum and difference circuit 80 to produce a sum
signal R.sub..SIGMA. and a difference signal T.sub..delta. . The
difference signal is treated in the same manner as at 70 or 72 of
FIG. 8, the separate phase-shifter channels for the reference phase
82 and the shifted phase 84 being again shown in FIG. 9. The
respective polarities of the reference and phase-shifted difference
signal T.sub..delta. are fed to fixed voltage dividers at 86 and 88
and the attenuated outputs are fed to summers 90 along with the sum
signal T.sub..SIGMA. from the reference-phase channel 91 producing
output presentation signals for the pre-selected angles
.phi..sub.1, .phi..sub.2, etc., for which the taps on the
attenuators or dividers 86 and 88 are designed.
Where the invention is employed in standard stereo FM broadcasting,
the function of the sum and difference circuit shown in FIG. 9 at
80 is performed in the standard stereo matrixing, and the circuit
80 may be omitted in decoding. It will be observed that such sum
and difference signals T.sub..SIGMA. and T.sub..SIGMA. may be
directly formed from source signals and employed as transmission
signals without formation of signals T.sub.L and T.sub.R, being
formed substantially as follows: ##SPC3##
The transmission signal pair T.sub.L and T.sub.R contains exactly
the same information as the transmission signal pair T.sub..SIGMA.
and T.sub..delta. , and these signal sets are readily convertible
from one form to the other in either direction without any
alteration of the available information content. Although these two
forms of the same signal information are normally the most useful
and simplest in equipment implementation, other transmission signal
pairs identical in overall information content and ready
convertibility to and from these specific forms may be devised and
will be understood to be included in the expressions above.
If so desired, individual presentation signals may, after
formation, be "touched up" in accordance with listener preference.
For example a particular listener may find the overall effect more
pleasing with further phase shifting of one or more of the
presentation signals after the formation thereof (not shown). As
another example, directional effects may be emphasized by auxiliary
signal treatment of the same type heretofore employed with other
coding and decoding systems, such as varying the amplification of
amplifiers feeding particular loudspeakers to increase apparent
"contrast" or sound-source localization for certain types of
sounds.
It will be observed that the encoded transmission signals are
readily useable with existing reproduction equipment having no
provision for decoding of multidirectional signals. The sum of the
two transmission signals is the simple sum of all of the source
signals in their original phase. Thus employment of the
transmission signals in the sum-and-difference mono-compatible
matrixing of stereo FM broadcasting, or reproduction of an encoded
stereo disc recording on a monaural phonograph, produces perfect
monaural reproduction. The employment of the two encoded channels
as the left and right channels of conventional stereo reproduction
produces only slightly less apparent left-right separation than a
conventional stereo recording (as in prior systems for quadrasonic
encoding and decoding with two-channel transmission).
If so desired, provision may be made in the decoder for
artificially encoding ordinary stereo signals containing no
directional information, so that such program material is
reproduced in the multidirectional speaker system in a manner
generally resembling the reproduction of signals wherein the
further directional information is encoded. Ordinary stereo signals
correspond to source signals at left front, LF, and right front,
RF. There is shown in FIG. 10 an adapter which may be substituted
for the sum and difference circuit 80 of FIG. 9, for example by a
switch on the decoder, to produce a listener effect or sensation
similar to that of direction-encoded signals having source-signal
components only from these directions. The ordinary stereo signals
are fed to respective 45.degree. phase slitters 92 and 94 to
produce a sum signal T.sub..SIGMA. in reference phase and a
difference signal T.sub..delta. in quadrature phase.
It has previously been mentioned that the selection of the two
transmission signals for direct reproduction at L and R locations,
respectively, is of significance only for compatibility with
conventional stereo equipment having no decoding provision. In its
broader aspects, the invention may be employed in applications
wherein stereo compatibility is unimportant. For example, the
invention may be used for the sole purpose of conserving tape
space, and thus extending playing time, in the general type of
recording now done in four or more discrete tape channels. By
compressing the information into two recording channels and then
expanding in playback, much greater utilization of tape space is
made. In such use of the invention the reference direction of the
bearing-angles used in encoding may be chosen more or less
arbitrarily, and the directions represented by the two transmission
signals are accordingly equally arbitrary, so long as they are
selected in diametric opposition.
The particularized embodiments of the invention thus far described
are confined to those designated for use with the two-channel
transmission systems which are currently standard for stereo
broadcasting and disc recording. However the broader aspects of the
invention are of wider application. The two-channel transmission
thus far described is merely a specific application of principles
which may be advantageously employed for reproducing directional
audio information with larger numbers of channels than two. By
employment of the invention, the results obtainable with
transmission limited to the two channels used in conventional
stereo reproduction are otpimized. However, in further accordance
with the invention, a larger number of channels may advantageously
be employed. A primary use for a larger number of channels is to
sharpen the directionality pattern for any given speaker array,
i.e., to reduce the cross-talk which is an unavoidable consequence
of employment of a number of loudspeakers larger than the number of
transmission channels. But the invention in its broader aspects may
be employed even where the number of transmission channels is equal
to or greater than the number of required presentation signals, for
the purpose of permitting "rotation" of presentation signals, such
as in reproduction of a four-track tape recording recorded for
"2-plus-2" loudspeaker presentation on loudspeakers arranged in a
"1-2-1" orientation, as later seen.
Understanding of the application of the invention to numbers of
channels greater than two will be facilitated by first considering
certain aspects of the performance and underlying theory of the
two-channel system already described. It may be seen upon study
that the essence of the advantageous novelty stems from the fact
that the sum of all products of the function of .theta. applied to
the source signals at bearing angles .theta. in formation of each
transmission signal and the function of .phi. applied to that
transmission signal in the formation of each presentation signal at
bearing angle .phi. is a single-variable 360.degree. repetitive
function of the difference between the angles .theta. and .phi.
having a maximum absolute value at a reference difference angle, a
relatively absolute value at the diametrically opposite difference
angle, and absolute values at intermediate angles symmetrical with
respect to the axis thus defined. It is this characteristic which
imparts the "rotatability" or "universality" of the loudspeaker
patterns for which the transmission signals may be decoded.
It will be obvious that all functions which satisfy these criteria
are not of wholly equal merit as regards simulation of
discrete-channel direct reproduction in psychoacoustic effect. All
other factors being equal, it is desirable that the amplitude or
absolute value of the overall reproduction function have a zero or
null at 180.degree. from the maximum. Likewise, all other factors
being equal, it is desirable that the amplitude pattern decrease as
rapidly as possible from its maximum value, which occurs where
.theta. equals .phi., i.e., where the difference angle .alpha. is
zero. Further, again with all other factors being equal, it is
desirable that phase differences between the appearances of any
given source sound in the various presentation signal be minimized,
i.e., that the overall reproduction have a minimum of relative
phase difference.
The relative importance of these three factors in producing the
illusion of presence at the actual performance is a psychoacoustic
matter which is presently incapable of quantitative evaluation. It
has been experimentally established that the reproduction produced
by the two-channel matrixing of the above-described embodiments is
more satisfactory than with other matrices for the same purpose.
The performance may be described in terms of the factors of merit
above by the following: The pattern demonstrates a complete null at
180.degree., an amplitude reduction of -3 dB at 90.degree. (and of
course 270.degree., these being a convenient point of reference for
measuring pattern "sharpness"), and no component is presented with
a phase difference of as great as 180.degree. from any other, any
components which are reproduced with a difference of phase
approaching 90.degree. from their original relative phase being
essentially negligible in amplitude. The employment of overall
functions which are better in one respect, but at the sacrifice of
another, is accordingly within the broad purview of the invention,
although it can be shown from information theory and sampling
theory that the reproduction information given by mixing and
re-mixing coefficients determined as above is as accurate as is
possible with only two transmission channels.
The characteristics or performance factors just described can be
substantially further improved by applying the same general
principles in the construction of transmission signals for three or
more transmission channels. Such applications of the principles of
the invention may be roughly divided into two categories in their
relation to the two-channel embodiment already described: (1)
systems employing one or more auxiliary channels or transmission
signals in addition to the two transmission signals already
described and (2) systems which employ three or more transmission
signals which display the same type of mutual symmetry as the
T.sub.L and T.sub.R signals of the two-channel system.
Three-channel (and further multiple-channel) systems of the first
type mentioned above may be described as "compatible" with the
two-channel system. A typical current utility of such embodiments
of the invention is in the production of threetrack or four-track
tape recordings which may be played back, with suitable decoding,
with any desired multiple array of speakers or may, alternatively,
be played back as ordinary stereo recordings by equipment which
cannot utilize the auxiliary recorded channel or channels. At such
future time as disc recording and broadcasting may be provided with
more than two signal channels, such auxiliary signals may likewise
be employed in these media for similar purposes.
To maintain the ability to decode for varying speaker arrays, the
encoding and decoding of the auxiliary channel must be such as to
maintain the above-described essential characteristics of the
overall transmission or presentation function. In principle, it may
be possible to devise third-channel transmissions which may be
decoded along with the two primary or basic transmission signals by
devising complex decoding for all three channels which departs
completely from the two-channel decoding in producing a desirable
overall playback function in which the difference angle .alpha. is
the sole variable. However it is found possible to preserve the
same general manner of decoding of the two channels T.sub.L and
T.sub.R and merely add to each presentation signal the auxiliary
information contained in the coded and decoded auxiliary
transmission signal. In order to do this, it is necessary that the
encoding and decoding of the auxiliary transmission signal (or
signals) produce an added component for the presentation signal
which is itself a function solely of the difference angle. The
simplest and most desirable manner of utilizing a third channel is
to employ an encoding function of .theta. for production of the
third transmission signal which, when multiplied by the conjugate
decoding function of .phi., itself produces a product which is a
single-variable function of the difference angle and which, when
added to the presentation signal function which results from the
two-channel transmission, increases the sharpness of the amplitude
maximum in the pattern. These requirements for the auxiliary
channel are met by the employment of an appropriate exponential
function of .phi. in encoding and its conjugate function of .phi.
in decoding. The addition of a third transmission signal T.sub.T
using a mixing coefficient proportional to
e.sup..sup.-j.sup.[.sup..theta. .sup.+ .sup..pi./2.sup.] for each
siganl S.sub..theta. and a remixing coefficient proportional to
e.sup.j .sup.[.sup..theta. .sup.+ .sup..pi. /2.sup.] in forming the
added component for each presentation signal P.sub..phi. produces a
product function of the difference in angles which, when added to
the basic two-channel presentation function, substantially sharpens
the directional effects. The overall presentation signal is
##SPC4##
With this overall playback function, all sound sources are produced
in all speakers in their original relative phase, and the amplitude
for an angle difference of 90.degree. (or, of course, 270.degree.)
is about 10 dB less than the maximum at 0.degree..
The auxiliary signal T.sub.T thus formed may be employed with
either the T.sub.L and T.sub.R transmission signals of equations
(1) or the transmission signals T.sub..SIGMA. and T.sub..delta. of
(4) above. The overall playback function thus obtained, although
improving the pattern in the respects just mentioned, produces a
signal component at 180.degree. of the same magnitude as the signal
component at 90.degree., i.e., about -10 dB from the maximum at
0.degree.. This "backlobe" may be eliminated by a simple
alteration. Considering the T.sub..SIGMA. and T.sub..delta. form of
transmission, of the T.sub..delta. and the T.sub.T signals are
attenuated by the square root of one-half, but without change in
T.sub..SIGMA. , and decoding by conjugate functions of .phi. is
carried out, the resultant overall transmission function is
##SPC5##
This overall reproduction function produces presentation signals
free of phase shifts and with a null at 180.degree., the magnitude
at 90.degree. being down 6 dB from the maximum at 0.degree.. The
same result is of course obtained with appropriate partial blending
of the T.sub.L and T.sub.R signals previously described, and the
same attenuation of T.sub.T. Where the basic pair of transmission
signals is thus modified, the performance on equipment not capable
of utilizing the third channel is obviously impaired. Accordingly,
the recorded or broadcast sets of transmission signals will not
normally include this alteration. The modified set of transmission
signals is preferably generated in the decoder from the unmodified
signals as recorded or broadcast.
The overall transmission or presentation equation set forth above
resulting from the modified transmission signals has a coefficient
expression shown in brackets which may also be written as
1 + cos (.phi..sub.i - .theta..sub.k)
This will be seen to be of the same form as the equation (5)
coefficient for the unmodified three transmission signals, each
overall presentation signal being expressable as ##SPC6##
where m is the square of the attenuation factor used in forming the
modified T.sub..delta. and T.sub.T. Appreciable variation in
details of reproduction characteristics is obtained by selection of
m. As m is varied in the range from 0.5 to 1.0, the "backlobe"
earlier mentioned is re-introduced, but the "90.degree. separation"
is simultaneously improved as indicated numerically earlier. With m
having an intermediate value of 0.707, the 90.degree. separation is
7.66 dB and the backlobe level is 28.3 dB below the 0.degree.
maximum. The choice of the constant m thus involves a tradeoff of
desirable pattern characteristics which is incapable of evaluation
as regards psychoacoustic effectiveness to the listener, and the
three-channel decoder is desirably provided with means for
adjustment by the user of the factor m above defined within the
range of 0.5 to 1.0. It will be observed that where the factor
.sqroot.m is introduced into the transmission signals at the
decoder, and the conjugate functions thereupon immediately applied
for decoding, the latter also of course including the factor
.sqroot.m, the two successive attenuations by the factor .sqroot.m,
may be replaced by a single attenuation by the factor m, as by
ganged attenuator potentiometers at the inputs for the unmodified
T.sub..delta. and T.sub.T signals, whereby the user may select a
value of m between 0.5 and 1.0.
The same general principle may be employed in further adding a
fourth channel for still further increasing the "contrast" between
the amplitude of reproduction of a source signal from a loudspeaker
in a position corresponding to the original position of the source
and the amplitude of its reproduction from other loudspeakers,
i.e., in further sharpening of the overall presentation signal
functions of (5). A fourth channel addition to the three channels
described above which meets the criteria already described is the
transmission signal T.sub.Q formed as follows: ##SPC7##
Such a function may be produced by summing the outputs of two
quadrupole microphones (each with one dipole pattern opposed in
phase to the other dipole pattern) relatively rotated by
45.degree., with the output of one quadrupole shifted in phase by
90.degree.. Alternatively (or as a supplement) mixing circuits
obtained by appropriate modification of those previously described
may be employed. An attenuation factor equal to the square root of
a constant m may be applied to the transmission signals T.sub.T and
T.sub.Q in the formation and conjugate-function decoding of these
auxiliary transmission signals. The overall presentation signals
are in this case of the form: ##SPC8##
The phase relations of the source-signal components in each
presentation signal are the same as in the two-channel case.
However the 90.degree. separation is vastly improved, as now
seen.
The effects of variation of m with the fourth channel added are in
broad terms generally similar to those of the corresponding
variation in the three-channel case already discussd. For a value
of m of 0.333, the pattern is of the cardioid type but the
90.degree. separation from the maximum at 0.degree. is 9 dB. For a
value of m of 0.5, the null at 180.degree. is preserved but very
small backlobes (-23.9 dB) appear in the adjacent regions; the
90.degree. separation is 12.6 dB. With a value of m of 1.0, nulls
appear at both 90.degree. and 180.degree., but there are noticeable
magnitudes (-11.3 dB) at about 130.degree. in each direction from
the 0.degree. maximum. The factors involved in selection of m by
the listener are generally similar to those in the three-channel
case, and it is desirable to provide the listener with adjustment
of this factor in the range from 0.33 to 1.0.
As will be evident, the principles of the invention may be further
extended to still higher numbers of channels while preserving the
two basic transmission signals T.sub.L and T.sub.R for reproduction
on equipment not capable of using the auxiliary channels.
In addition to such addition of auxiliary channels for the
two-channel system first described herein, which may be considered
as "compatible" additions to the basic two-channel system, the
principles of the invention may be employed for multiple channels
which are all associated with particular bearing angles in the same
general manner as the signals T.sub.L and T.sub.R are identified
with the directions "left" and "right."
Understanding of this aspect of the invention will be promoted by
first considering further theory of the basic two-channel
embodiment earlier described. In the discussion up to this point,
bearing angles .theta. and .phi. have been considered as measured
from the front center (or rear center) position. As already
described this produces slightly different encoding functions for
the "left" and "right" transmission signals T.sub.L and T.sub.R,
which are unaltered in producing presentation signals for speakers
at these opposed side locations. If there be considered an angle
.theta.' for each sound source, measured from the "left" direction
or bearing angle for T.sub.L and from the "right" direction or
bearing angle for T.sub.R, the encoding function or mixing
coefficient function for both of these transmission signals may be
expressed as:
1 + cos .theta.' + j sin .theta.' = 1 +
e.sup.j.sup..theta..sup.'
For reasons shortly apparent, this may advantageously be now
rewritten in the form
1/2 + 1/2 cos .theta.' + 1/2j sin .theta.'
(It may have already been observed that this fractional
representation has merely been disregarded for simplicity
heretofore even in instances where its presence would be required
for rigorousness, for example in dropping a multiple "2" in
deriving equation (3) from equations (1) and (2)).
The above expression for the forming of each transmission signal
from source signals, using the direction to which the transmission
signal corresponds as the reference for the bearing angle of the
source, may be designated f.sub.2 (.theta.'), where the subscript
indicates the encoding function for each of two channels.
In similar fashion, the encoding function f.sub.2 (.phi.') for each
transmission channel in forming each presentation signal may be
stated as
1/2 + 1/2 cos .phi.' - j sin .phi.'
where .phi.' is the bearing angle of the presentation signal with
reference to the direction to which the transmission signal
corresponds. Th overall or summed presentation signal function is
of course not affected by this alteration of reference point used
in the encoding and decoding, being the same as the encoding
function except for the difference-angle argument .alpha..
Similar encoding functions (and conjugate decoding functions) may
be employed for larger numbers of transmission signals
corresponding to equally spaced directional angles. For three
channels, at 120.degree. intervals, the encoding function is
f.sub.3 (.theta.') = 1/3 + 2/3 cos .theta.'
and the decoding function of .phi.' is identical (the function
having no imaginary term). The overall presentation signal function
is again identical with the encoding function except for the
difference-angle argument. It will be seen that this overall
function is exactly the same as that obtained with the unmodified
"compatible" three-channel system set forth above at (5). It may be
demonstrated that the "compatible" and "equal-spaced" transmission
signals are each linear combinations of the other, i.e., derivable
from each other by reversible methods of linear combination which
produce no change in the information content.
For four channels or transmission signals (primary transmission
signals at each 90.degree.) the encoding function for each is
f.sub.4 (.theta.') = 1/4 + 1/2 cos .theta.' + 1/4 cos 2.theta.' +
1/4j sin 2.theta.'
and again the overall reproduction is the same as with the
"compatible" four channel system (unmodified) earlier discussed
which is related by linear transformation.
Such encoding is particularly useful in the making of
discrete-signal four-track recordings, which can be played back
with any desired speaker array.
It may be shown that further extension of this specific method of
encoding and decoding in accordance with the invention may be made
to any number n of channels representing equally spaced bearing
angles by the expression, for any odd number of channels,
f.sub.n (.theta.') = (2/n)[1/2 + cos .theta.'+ cos 2.theta.' + . .
. + cos (n-1/2) .theta.']
and by the expression, for any even number of channels,
f.sub.n (.theta.') = (2/n) [1/2 + cos .theta.' + cos 2.theta.' + .
. . + cos (n-2/2).theta.'] + (1/n) [cos (n/2).theta.' + j sin
(n/2).theta.']
As will be apparent, the larger the number of channels available,
the larger the variety of particular encoding and conjugate
decoding functions which may be devised for practicing the basic
aspects of the invention, and the embodiments described above are
merely illustrative of the simplest, particularly with numbers of
transmission channels greater then 2. More complex functions,
employing numerical factors in coefficients of various components
more or less analogous to the single factor m earlier discussed,
may be devised, as well as the forms of linear combinations.
Persons skilled in the art will accordingly readily devise many
further variants of the specific embodiments of the invention
herein selected for illustration and description. The protection to
be afforded the invention should thus extend to all utilizations
thereof as defined in the appended claims, and equivalents
thereto.
* * * * *