Loudspeakers, Mutual Coupling and
Keith R Holland
lSVR,
University of Southampton,
Philip R Newell Moana,
The use of loudspeakers in pairs
for the reproduction of two-channel stereo gives rise to mutual coupling effects
which compound the usual loudspeaker / room interface problems. In this paper,
the performance of pairs of idealised loudspeakers in various idealised
acoustic environments is discussed and conclusions are drawn concerning the
reproduction of centrally-panned phantom images.
1 Introduction
The search for the "perfect loudspeaker" has
occupied the minds of audio manufacturers and enthusiasts alike for many years.
Most would agree on many of the
specifications of such a device: a flat frequency response, zero distortion
etc., but the requirements for perfect stereo reproduction are far less
obvious. Even if such devices existed, the use of these perfect loudspeakers in
stereo pairs in real rooms would almost always fail to live up to expectations
due to mutual coupling effects which compound the usual loudspeaker / room
interface problems.
The influence of room boundary walls on the power
output of a loudspeaker has been well researched and documented. In [1],
Allison shows how the presence of a single boundary wall increases the power
output of a loudspeaker by 3dB at low frequencies, and that introducing two
more boundaries gives a net increase of 9dB. More recently, Ward and Angus [2]
have extended the concept further to include all six boundary walls. The
significance of these findings in the context of this paper is that the
presence of a single boundary gives rise to the same sound field as would the
introduction of a second, identical loudspeaker placed at the mirror-image
position in the absence of the wall. It is therefore logical to assume that
introducing a second, identical real loudspeaker - the second of a stereo pair
- would also increase the power output of the first loudspeaker. However,
whereas the influence of room boundaries on loudspeaker power output is signal
independent and may be predicted and corrected for by loudspeaker design and /
or electrical equalisation, the influence of one loudspeaker on the other in a
stereo pair is very dependent upon
the exact nature of the (independent) signals fed to the two loudspeakers. For
example, when a stereo pair of loudspeakers is reproducing a fully left- or
fully tight-panned signal, only one loudspeaker is operating, so, 'perfect'
sound reproduction is possible. For centrally-panned images however, both
loudspeakers are receiving the same signal, and interference effects give rise
to a sound field that is very dependent on position and frequency.
When it is considered that in most
modern stereo recordings, much of the important information carrying sounds,
such as lead vocals and instruments, narration or dialogue, are panned
centrally between the loudspeakers, it is a shame that the reproduction of
these sounds is almost always compromised compared to those sounds which are
panned fully left or right. It is the objective of this paper to investigate
the problems associated with the reproduction of the central phantom image over
a stereo pair of loudspeakers, and to attempt to shed some light on how these
problems may be reduced or overcome.
To attempt to analyse the entire loudspeaker pair /
room interface problem would be an enormous task and would yield results that
only really applied to the particular set of conditions being modelled; what is
required is a simpler, more general approach with the number of variables
reduced to a minimum. To this end, this paper is concerned with examining the
performance of idealised "perfect" loudspeakers when used in pairs
for reproducing stereo signals, with particular reference to the reproduction
of the central phantom image. The behaviour of velocity-source and
pressure-source loudspeaker pairs is analysed in some detail under both freefield (anechoic) and reverberant acoustic conditions.
2 The Analysis of Perfect Loudspeakers in Perfect
Rooms
Consider two idealised acoustic environments - the
anechoic chamber and the reverberant chamber - both containing a single,
perfect, omnidirectional, velocity-source loudspeaker
(loudspeaker A). The response at any point in the anechoic chamber is dependent
upon the pressure response of the loudspeaker (the sound pressure at a point
per unit electrical input) which, as the loudspeaker is omnidirectional,
is the same everywhere. In the reverberant chamber, the response at any point
is the sum of an infinite number of reflexions from
the walls, which all arrive with different time delays (a diffuse field). The
reverberant response therefore depends upon the power response of the
loudspeaker (the total sound power radiated per unit electrical input), and is
thus also the same everywhere. The power output of any source can be found by
integrating the anechoic responses over all angles, so the sound power response
of an omnidirectional loudspeaker is the same as the
pressure response; a flat response will result everywhere in both the anechoic
chamber and the reverberant chamber.
2.1 Two Velocity-Source Loudspeakers in an Anechoic
Chamber
Now introduce a second perfect loudspeaker into the
anechoic chamber (loudspeaker B) and feed it with the same signal as the first,
such as is the case for a centrally panned stereo image. The response will no
longer be flat everywhere because of the interference between the sound fields
radiated by the two loudspeakers - the combined output is no longer omnidirectional. However, at any point along a centre-line,
equidistant from the two loudspeakers (the stereo 'hot-seat' line), the two
sound fields will add constructively at all frequencies giving a flat response
6dB higher in level than that of one loudspeaker alone. At all other points,
the sound fields will constructively or destructively interfere depending on
the path length differences and the wavelength (frequency) of the sound - a
comb-filtered response will result. The sound field can be calculated as the
sum of the pressures generated by the two loudspeakers and this pressure can be
compared to that generated by a single loudspeaker of the same output, placed
midway between the pair:
where R, rA and rB are the distances from the point of interest to the
central loudspeaker, loudspeaker A and
loudspeaker B respectively (see
figure 1) and k = ù/c0 is the
free-space wave number at an angular frequency of m radians per second. Figure
2 shows two typical responses of a pair of loudspeakers at positions away from
the centre-line relative to that of a single loudspeaker placed midway between
the pair.
2.2 Two Velocity-Source Loudspeakers in a Reverberant
Chamber
If we introduce the second loudspeaker into the
reverberant chamber. The response is now the same everywhere and is dependent
upon the combined power response of
the two loudspeakers. A simple realisation of an omnidirectional
source is that of a pulsating sphere. The sound power radiated by such a source
can be written
where a is the radius of the sphere, u(a) is the
surface velocity of the sphere, p(a) is the acoustic pressure on that surface,
S is the surface area, 9t{ ) denotes the "real part of and' denotes the
complex conjugate. For a pair of velocity-source loudspeakers, u(a) is fixed
and p(a) is the sum of the pressure generated by loudspeaker A due to its own
velocity and that generated by loudspeaker B
on the surface of A. It should be noted that only the direct sound from B affects the power output in the
reverberant chamber - the reverberant field is assumed to be diffuse and
therefore has random phase and a net effect of zero; the power output of the
loudspeaker pair is therefore the same as under anechoic conditions. The
combined power output of the pair of loudspeakers, relative to that of a single
loudspeaker is then
where d is the distance between the two sources. A
derivation of equation (3) can be found in the appendix. Figure 3 shows the
combined power output of a pair of velocity-source loudspeakers relative to the
power output of one of the loudspeakers operating in isolation.
The important features to note about figure 3 are
that, in agreement with [1] for a single loudspeaker and reflective wall, at
high frequencies the power output of the pair of loudpeakers
is approximately +3dB (double) relative to that of a single loudspeaker -
entirely as expected, and that at low frequencies the increase in power output
is nearer +6dB (four times). The "magic" doubling of power output at
low frequencies may be explained using the concept of mutual coupling.
2.3 Mutual Coupling
The concept of mutual coupling
between loudspeakers is familiar to anyone who has mounted two loudspeakers
close together. The power output of the two loudspeakers is approximately four
times (+6dB) that of a single loudspeaker. Also, if you double the area of the
diaphragm of
a loudspeaker drive-unit, given the same diaphragm
velocity, the power output will again increase by +6dB. Reference to equation
(2) shows that introducing a second loudspeaker close to a first will
approximately double the pressure on each of the diaphragms, thereby doubling
the power output of both loudspeakers.
What is perhaps less obvious however, is how
introducing a distant second
loudspeaker can double the power output of a loudspeaker. For the 3m separation
and 0.15m radius of the pair of loudspeakers in the above examples, the
magnitude of the pressure on loudspeaker A due to the operation of loudspeaker
B is approximately one twentieth of the pressure on A due to its own velocity.
How can an increase in pressure of 5% cause a doubling of power output? The
answer lies in the phase of the two pressures. At low frequencies, the pressure
on the surface of A due to its own velocity is almost in phase quadrature with the velocity - the radiation impedance is
almost totally reactive - whereas that from B
arrives almost in-phase with the
velocity due to the propagation distance involved. Equation (2) tells us that
it is only the in-phase part of the pressure that is responsible for power
output. As the distance d is decreased, the magnitude of the pressure due to
the second source increases but its phase approaches that of the pressure due
to the velocity of the first source - the power increase remaining at +6dB but
extending higher in frequency - until the "two close loudspeakers"
situation exists. As can be seen from equation (3), the frequency up to which
the mutual coupling occurs is determined by the distance between the two
sources; as the propagation distance approaches half a wavelength the phase of
the pressure from the second source is no longer in phase with the velocity.
The distance over which mutual coupling occurs is known as the extent of the
hydrodynamic near field of the loudspeakers.
2.4 Transient Signals
The concept of mutual coupling is fine for explaining
the power increase with steady-state, single tone signals. However, under
transient excitation, the two loudspeakers operate simultaneously and by the
time the pressure from loudspeaker B has
reached loudspeaker A, loudspeaker A has
stopped moving. If they are velocity-source loudspeakers, the presence of the
delayed transient pressure from B can have no effect on the sound radiated from
A, as this transient has already left the loudspeaker. However, the
steady-state and transient responses of any linear system are linked by the
Fourier transform pair, so any change in response to steady-state excitation must be reflected in the transient
response, so what has happened to the mutual coupling with transient
excitation?
In order to explain the transient response it is
necessary to study the steady-state directivity of the loudspeaker pair. Figure
2 shows the response of a pair of loudspeakers at two different positions away
from the centre-line in an anechoic chamber. Two important features of the two
responses are that the peaks and dips in response occur at different
frequencies for different positions and that the responses are similar at low
frequencies. It can be shown that the combined power response of the two
loudspeakers is proportional to the sum of the (squared) anechoic responses
over all angles, ie the sum of an infinite number of
responses of which those in figure 2 ace typical examples. At low frequencies,
all of the responses are similar and they sum to give +6dB increase in power
output compared to a single loudspeaker. At higher frequencies however, the net
result of summing all of the (different) comb-filtered responses is, on
average, a +3dB increase compared to a single loudspeaker. The result of
integrating the squared responses (actually the intensities) over all angles is
therefore the power response shown in figure 3. Figure 4 shows the (far-field)
polar directivity response of a pair of loudspeakers separated by 3m. It can be
seen that integration of the (squared) polar diagrams would yield a result
close to 2 (+6dB) at low frequencies and approximately 1.4 (+3dB) at high
frequencies. Thus the mutual coupling phenomenon can be explained easily in
terms of the directivity of the loudspeaker pair.
At positions along the centre-line between the two
loudspeakers, the transients from the two loudspeakers arrive together and
superimpose perfectly giving a transient of double the height; +6dB at all
frequencies. At all other positions, they are time-displaced and therefore do
not sum to give a double height transient. The Fourier transform of a double
transient signal is a comb filtered response like those shown in figure 2.
Integration of the intensity of the double transient over all angles therefore
yields the same result as for the steady-state response, but integrated over
all of the frequencies contained within the transient signal. It is clear
therefore that narrowing the transient in time increases the bandwidth, narrows
the angle in space over which the two transients overlap, and reduces the
significance of the low frequency gain to the overall power.
2.5 Pressure-Source Loudspeakers
The above discussion on directivity and transient
response would seem to indicate that replacing the velocity-source
loudspeakers, for which the source velocity is independent of the pressure load
exerted upon it, with pressure-source loudspeakers, for which the velocity
changes with changing pressure load so as to maintain constant pressure, would
have little effect on the combined power output. However, consideration of the
mechanism of mutual coupling suggests that the increase in pressure due to a
second loudspeaker would cause a reduction in velocity which would reduce power
output. The derivation of the equivalent of equation (3) but for pressure-source
loudspeakers is also in the appendix and this shows that the combined power
output of a pair of pressure source loudspeakers, relative to that of a single
loudspeaker is
thus in the limit of d » a, pressure-source loudspeakers do demonstrate mutual coupling to the same degree as
velocity-source loudspeakers. However, as the source size is increased or the
spacing between the loudspeakers is decreased, the mutual coupling reduces
until it is zero for the "two close loudspeakers" case, and only a +3dB
power increase is observed. The small additional pressure load exerted by a
distant second loudspeaker only changes the velocity by a small amount, despite
the increase in power output, but the doubling of the pressure load exerted by
a close second source reduces the velocity to one half. Figure 5 shows the
combined power output of a pair of pressure-source loudspeakers of the same
size and spacing as the velocity source loudspeakers shown in figure 3, and
figure 6 shows the combined frequency response at 20° away from the centre-line
to compare with the first plot in figure 2.
3 Discussion and Practical Implications of Results
The above analysis of the mutual coupling between a
stereo pair of perfect loudspeakers in ideal environments is interesting from
an academic point of view, but how do the results relate to the usual situation
of imperfect loudspeakers in imperfect rooms? When a single loudspeaker is
operated in a typical room, mutual coupling occurs between the loudspeaker and
each of the mirror image loudspeakers in each wall; there is also mutual
coupling between each mirror image and each other mirror image and so on... So
to worry unduly about the coupling between the two loudspeakers in a stereo
pair seems, at first thought, a bit silly. However, the main objective of this
paper is to investigate the phantom central image, and it is in the
reproduction of this that mutual coupling between the loudspeakers themselves
becomes important. If there are a certain number of significant, coupled sources
in a given room when one loudspeaker is operated, this number will always at
least double when two loudspeakers are operated; most rooms behave in a more or
less semi-reverberant manner, so the combined power output of the loudspeakers
is of importance. Thus there will always be a significant difference between
the reproduction of a fully left- or right-panned image and the
centrally-panned phantom image.
3.1 The Pan-Pot Dilemma
In an anechoic chamber, a mono-eared listener sat
directly on the centre-line between a stereo loudspeaker pair, listening to a
broad-band sound that is panned from fully left, through centre, to fully
right, hears no change in timbre or level (head related transfer functions
apart) if the panpot reduces the signal level by -6dB
to each loudspeaker in the central position. If that listener moves away from
the centre-line, the sound will be perceived as going from "flat"
through "coloured" to "flat" as it is panned, due to the
poor directivity of the stereo pair giving rise to comb-filtering (see figure
2); the nature of the coloration being different for different off-centre
positions. This would, of course, be accompanied by the usual "break
down" of the stereo illusion associated with off-central listening. The
only problem experienced by a listener in the hot-seat in an anechoic chamber
is that most of us have a head with a "working" ear on both sides, so
neither ear is on the centre-line. Also, the diffraction around the head is
different for a single frontal source than for a phantom image. The
comb-filtering associated with having ears that are some 100mm away from the
centre-line has its first dip at around 2kHz under typical listening
conditions.
In the reverberant chamber, the same signal would be
perceived as having the same "flat" spectrum as in the anechoic
chamber when panned fully left or fully right (any information content in the
signal would be severely masked by the reverberation, however), but when the
signal is panned to the central position, it has a spectrum similar to that in
figure 3, with a +3de rise at low frequencies. If the same -6dB pan-pot law is
used, the low frequency content of the signal will remain the same, as it is
panned, but the rest of the signal will be reduced in level by -3dB at the
central position. One can imagine a suitable pan-pot law for use in the
reverberant chamber which reduced the low frequencies by -6dB and the higher
frequencies by -3dB at the central position, thus maintaining the
"flat" spectrum at all positions of the panned image, but listening
to stereo reproduction in a reverberant chamber has limited appeal!
Clearly, the ideal pan-pot law depends upon the
acoustics of the room in which the sound will be reproduced. Real rooms behave
in a manner somewhere between anechoic and fully reverberant, so some
compromise is necessary. Many mixing console manufacturers will produce
different pan-pot laws for different applications, though they usually opt for
a -4'hdB compromise, which produces only a 1'hdB worst case error. The fact that
this seems to work well is borne out by the number of recording engineers who
fail to realise that this situation exists at all. Regardless of the pan-pot
law chosen, in all situations, with the notable exception of a mono-eared
listener sat in the stereo hot-seat in an anechoic chamber, a centrally-panned
phantom source will be perceived as having a different timbre from a true
centrally mounted loudspeaker; a fact that has strong implications for stereo /
mono compatibility (see section 3.4). Amongst experienced recording engineers,
there is a saying: "pan first, then equalise"; there is wisdom in
this statement, even in perfect acoustic environments.
3.2 Specialist
Listening Room Design –
The Studio
Control Room
The importance of mutual coupling and the related
directivity problems associated with a stereo pair of loudspeakers (see figure
4) depends to a large extent on the acoustic treatment of a listening room. The
domestic end users of much recorded material usually have little control over
the acoustics of their listening environment, and many people these days listen
via headphones or in automobiles where the problems associated with
"normal" stereo reproduction do not occur. However, it is in the recording
studio where the creation and quality control of the recording is carried out,
and it is in the control rooms of these studios where the problems associated
with stereo pairs of loudspeakers are important, and where specialised acoustic
design is possible.
The anechoic chamber seems to offer the best
situation, provided listening is carried out in, or near, the stereo hot-seat.
The authors have been lucky to have experienced stereo reproduction over high
quality loudspeakers in the large anechoic chamber at ISVR;
it is a memorable
experience.
In truly reverberant condition, the total sound power
output of the pair of loudspeakers is maintained in the reverberant field,
irrespective of the fact that the interference between the loudspeakers causes
different, comb-filtered responses in different directions (see figures 2 and
4). However, once absorption is introduced into the room, the absorbent areas
rob the reverberant field of energy, either direct or reflected, which travels
in the direction of the absorbent surfaces. This absorbed energy will be
non-uniform in frequency content - even with "perfect" absorbers -
due to the poor directivity of the loudspeaker pair. Likewise, if reflective
surfaces are introduced into an otherwise "dead" room, they return
energy to the listener, once again, with a frequency balance which is dependent
upon the directivity of the loudspeaker pair. These problems do not occur when
only one omnidirectional loudspeaker is operated. So,
even in a world with perfect reflectors, absorbers and diffusers, we still
could not produce "accurate" listening conditions for the central
phantom image between two perfect loudspeakers in nonanechoic
rooms.
The "sister" of this
paper "A Proposal for a More Perceptually Uniform Control Room for Stereophonic
Music Recording Studios" by Newell & Holland [3].[ in our site also] puts forward strong arguments for what are
termed "Non-Environment" rooms. The idea behind these rooms is that the
side walls, rear wall and ceiling are made as absorbent as possible down to as
low a frequency as possible whilst the front wall and floor are hard and
reflective. The monitor loudspeakers are mounted in the hard front wall,
providing a rigid, diffraction-free baffle, and this surface along with the
hard floor also provide the "acoustic life" desired by the room
occupants. Such a room is ideal for optimised reproduction of the central
phantom image. The rooms are not at all reverberant, so the mutual coupling
problem does not occur, and the sound leaving the monitors can only be
reflected off of the floor which, being a horizontal surface, doe not reflect
the comb-filtered response to the listener.
3.3 Real Loudspeakers
So far we have considered only "perfect"
spherical omnidirectional loudspeakers. Most real
loudspeakers are omnidirectional at low frequencies
but are far from omnidirectional at higher
frequencies. The low frequency mutual coupling argument can be applied to real
loudspeakers with some confidence however. Equation (3) for example, only
requires a small change in its derivation for adaptation to baffled pistons in
place of pulsating spheres, and is identical in the limit of d » a.
Consideration of pressure-source loudspeakers shows that the finite mechanical
impedance of real loudspeakers also has little effect on the results. The
directivity of real loudspeakers at mid and high frequencies significantly
alters the directivity of the loudspeaker pair however, and this changes the
interaction with absorbers and reflectors, as discussed in section 3.2. As a
general rule, narrow directivity loudspeakers interact less with room acoustics
than wide directivity loudspeakers, whether considering a stereo loudspeaker
pair or simple mono reproduction. Under anechoic listening conditions, there
are no reflexions, so the only sound heard by a
listener is that which passes directly from the loudspeaker to the listener,
therefore there is no perceivable difference between a perfect omnidirectional loudspeaker and one which radiates a
uniform frequency response only in the direction of the listener; the omnidirectional loudspeaker is just wasting power.
Dipole loudspeakers, such as most electrostatics,
behave in a different manner. The dipole radiation pattern means that little or
no sound is radiated towards the other loudspeaker thus rendering them immune
to mutual coupling effects providing the stereo pair do not face each other.
Some room-related mutual coupling will still occur however, although to a lesser
extent than for monopole loudspeakers.
3.4 Stereo / Mono Compatibility and Surround Sound
Under almost all stereo listening conditions, mutual
coupling gives rise to a change in timbre of a sound as it is panned from fully
left or right, to centre. Given that most listening rooms can be described as
semi-reverberant, there may be a frequency equalised pan-pot law that could
apply some correction to the low frequency boost of the central image (although
not the directivity problems). The
frequency below which this low frequency cut should occur is determined by the
distance between the loudspeakers, and the amount of cut is related to the low
frequency reverberation time of the room. However, if such a pan-pot were used,
the resulting mix would not work correctly under non-average stereo listening
conditions such as headphones, portable stereos ("boom boxes") and
in-car audio. What is probably more important though, is how such a mix would
"fold down" to mono. The correct pan-pot law to use for mono compatible
stereo is the -6dB, voltage summing law described in section 3.1. Any stereo
mix that attemps to correct for mutual coupling under
stereo listening conditions will not be correct when summed to mono. This
situation is compounded when multi-channel surround sound systems are
considered. Figure 7 shows the combined power output of four loudspeakers
arranged in a rectangle of 3m x 4m. What is immediately apparent is that the
mutual coupling problem associated with a stereo pair of loudspeakers is compounded
with four loudspeakers to give a low-frequency boost of +12dB (16 times more
power) compared to a single loudspeaker. Remembering that this boost will
depend upon the room acoustics and the type of loudspeaker used, what form
should the surround sound mix take, and how will such a mix fold down to stereo
or even mono? This is a question of great importance for television.
One possible solution to the multi-channel
compatibility problem, and that of mutual coupling in general, could be the use
of a mono subwoofer. The subwoofer could reproduce the low frequencies below
the half-wavelength frequency thus eliminating the low frequency boost in
centrally-panned sounds. One problem with using a mono subwoofer is that the
path length from the mid-frequency loudspeakers and that from the subwoofer
will be different at different points in the room, giving rise to possible
crossover / localisation problems. A solution to this would be to keep the low
frequency loudspeakers in their stereo positions and to connect them together
electrically. The main disadvantage with the mono subwoofer though, is that it
cannot reproduce any out-of-phase low frequency stereo information. Such
information, even if not reproduced faithfully (a very rare situation), can
contribute to the feeling of ambience in live recordings or enhance special
effects in film soundtracks etc.
Most of the problems described in this paper are
greatly reduced by the adoption of a third, centre channel. The important,
information carrying central image would then be reproduced with the same
quality as the fully left or right images. Ideally, a new three-channel version
of stereo could be introduced, but existing centre-channel systems, such as
those adopted in some surround sound systems, can be effective. An additional
bonus to the use of a centre channel is an effective widening of the stereo
hot-seat, at least for centrally-panned images.
A completely different approach to stereo reproduction
may also alleviate the problems. Such a system, using a pair of closely-spaced
loudspeakers, is being researched by Kirkleby et al
[4]. The close proximity of the two loudspeakers means that any mutual coupling
that does occur, does so over a wide frequency range, and that the directivity
of the pair of loudspeakers is greatly improved.
4 Conclusion
This paper is concerned with two problems associated
with the reproduction of the important phantom central image via a stereo pair
of loudspeakers. One problem concerns the increase in power output of a
loudspeaker when a second loudspeaker is fed with the same signal, and the
other concerns the poor directivity of a widely-spaced loudspeaker pair and the
interaction of this directivity with the listening room.
Studies of the behaviour of pairs
idealised loudspeakers under idealised acoustic conditions show that the two
problems share the same cause but have different effects.
It is concluded that under almost all listening
conditions the timbre of a signal panned centrally between a stereo pair of
loudspeakers will differ from that from a centrally mounted mono loudspeaker
(or that from either of the stereo loudspeakers alone). The conclusions drawn
are shown to have a direct bearing on recording studio control room design as
well as compatibility problems between multi-channel, stereo and mono systems,
and serve to highlight the fact that two-speaker stereo is a very unstable
illusion.
5 References
[1] R F
Allison, "The Influence of Room Boundaries on Loudspeaker Power
Output", presented at the 48th Convention of the Audio Engineering
Society, May 1974 in "Loudspeakers, an Anthology, Vol. l-Vo1.25",
edited by R E Cooke, The Audio Engineering Society, 1980, p353-59.
[2] T Ward
and J A S Angus, "The Effect of a 6 Walled Room on Loudspeaker
Output", Proceedings of the Institute of Acoustics, Vol. 18, part 8,
Reproduced Sound 12, 1996, p253-61.
[3] P R
Newell and K R Holland, "A Proposal for a More Perceptually Uniform
Control Room for Stereophonic Music Recording Studios", presented at the 103rd
Convention of the Audio Engineering Society, September 1997.
[4] O Kirkleby,
P A Nelson and H Hamada, "The "Stereo Dipole" - Binaural Sound
Reproduction using Two Closely Spaced Loudspeakers", presented at the
102nd Convention of the Audio Engineering Society, March 1997, AES Preprint No. 4463
end