Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
LOCALIZATION USING DIFFERENT AMPLITUDE-PANNING METHODS IN THE
FRONTAL HORIZONTAL PLANE
Matthias Frank
Institute of Electronic Music and Acoustics,
University of Music and Performing Arts Graz
Graz, Austria
ABSTRACT
Amplitude panning is the simplest method to create phantom sources
in the horizontal plane. The most commonly employed amplitude-
panning methods are Vector-Base Amplitude Panning (VBAP),
Multiple-Direction Amplitude Panning (MDAP), and Ambisonics.
This article investigates the localization of frontal phantom sources
created by VBAP, MDAP, and Ambisonics (with and without max-
rE
weighting) at the central listening position in a listening experi-
ment. The experiment was conducted under typical non-anechoic
studio listening conditions and utilized pink noise and a regular
array of
8
loudspeakers for all methods. The experimental results
are compared to different predictors: a binaural localization model
using measured binaural room impulse responses, the direction
of the measured sound intensity vector, and the directions of the
simpler velocity and energy vectors. The article hereby addresses
the questions of how close the actually localized directions of the
different panning methods are compared to the desired directions,
and how good the predictors match the experimental results.
1. INTRODUCTION
Amplitude-panning methods use simple level differences between
the loudspeakers to evoke auditory objects between the loudspeak-
ers, so-called phantom sources [
1
]. Although the computational
effort is similar, the methods differ in their theoretical basis and
the number of loudspeakers they use for each phantom source.
This contribution examines perceptual differences between the
most commonly used amplitude-panning methods, in particular
the phantom source localization. This is done by employing ex-
isting experimental results from the thesis of the author [
2
] that
used vector-base amplitude panning, multiple-direction amplitude
panning, and Ambisonics with different weightings on the same
loudspeaker arrangement. Although there are some studies about
the localization of Ambisonics [
3
,
4
,
5
], comparisons to the other
panning methods are rare [
6
]. The experiment focuses on frontal
directions (with a maximum displacement from the median plane
of
45◦
) in order to compare the panning methods within the an-
gular range where human sound source localization works most
accurately [7].
The experimental results are compared to the directions of the
simple velocity and energy vector. Although the suitability of these
measures for the prediction of phantom source localization has not
been proven yet, they are often applied in practice for Ambisonics
decoder design [
8
]. This contribution examines their suitability and
compares them to a state-of-the-art binaural localization model and
measurements of the sound intensity vector.
The second section introduces the employed amplitude-panning
methods and their theoretical basis. The experimental localization
results for the panning methods are presented in the third section. In
order to examine the controllability of the phantom source location,
subjective variation is discussed and the results are compared to
the desired panning direction. Section four presents localization
predictors that are based on dummy head or microphone array mea-
surements at the listening position within the actual sound field,
as well as simpler predictors incorporating solely the loudspeaker
gains and positions. Finally, their predictions are compared to the
experimental results.
Throughout this contribution, the directions of L loudspeakers,
as well as the panning directions are expressed as unit vectors
θ= [cos(φ),sin(φ)]T
depending on the azimuth angle
φ
in the
x
-
y
plane, cf. Figure 1. The scalar weight
gl
of each loudspeaker
l∈ {1...L}denotes its adjustable gain.
x
g1
y
φ2
r·θ2
g2
g3
g4
g5
g6
g7
g8
Figure 1: Experimental setup in the reference coordinate system.
The smaller, gray loudspeakers are visible but inactive.
41
Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
2. HORIZONTAL AMPLITUDE-PANNING METHODS
All presented amplitude-panning methods are also applicable to
three-dimensional loudspeaker arrangements. However, this over-
view focuses on the two-dimensional case that is employed in this
contribution.
2.1. Vector-Base Amplitude Panning (VBAP)
Vector-Base Amplitude Panning (VBAP) [
9
] can be seen as the
generalization of the tangent law [
10
] for amplitude panning in two-
channel stereophony [
11
]. The tangent law is based on a simple
geometrical head model and is still the most popular panning law
for pairwise panning. In order to create a phantom source within
a loudspeaker pair located at
Lij = [θ
θ
θi,θ
θ
θj]
, VBAP calculates the
weights gij = [gi, gj]Tdepending on the panning direction θs:
gij =L−1
ij θs.(1)
Typically, a subsequent normalization of the gains is necessary to
keep the overall energy constant. The aperture angle of the loud-
speaker pair should not exceed
90◦
[
12
] resulting in non-negative
weights. To extend the panning range around one pair, more loud-
speaker pairs can be attached [9].
Basically, the number of active loudspeakers is depending on
the panning direction: two loudspeakers are active for directions be-
tween two loudspeakers and one is active for directions coinciding
with a loudspeaker.
2.2. Multiple-Direction Amplitude Panning (MDAP)
For a more uniform panning, those cases of VBAP with only one
active loudspeaker can be avoided. This is done by extending
VBAP to Multiple-Direction Amplitude Panning (MDAP) [13].
MDAP superimposes the results of VBAP for B panning direc-
tions uniformly distributed around the desired panning direction
θs
within a spread of
±φMDAP
. Typically, the maximum spread is
related to the loudspeaker spacing
∆φL
of a uniform loudspeaker
arrangement. In this contribution, MDAP is always used with
B = 10
panning directions uniformly distributed within a spread
of φMDAP =1
/2∆φL.
For this setting, three loudspeakers are active for most panning
directions, even for directions on a loudspeaker. If the panning
direction lies exactly in the middle between two loudspeakers, only
these two loudspeakers are active. In these special cases, MDAP
yields the same loudspeaker gains as VBAP.
2.3. Ambisonics
Ambisonics [
14
,
15
,
16
,
17
] is a recording and reproduction method
which is based on the representation of the sound field excitation
as a superposition of orthogonal basis functions. In the horizontal
case, these functions are the periodic trigonometric basis of the
Fourier series, the so-called circular harmonics. Their maximum
order
N
determines the spatial resolution and the number
2N + 1
of signals and minimum required loudspeakers.
For one source at a direction
θs
, the Ambisonic spectrum
yN(θs)
is calculated by evaluating the circular harmonics at
θs
This calculation is frequency-independent and assumes that all
sources and the loudspeakers lie on a circle of the same radius r.
The decoder derives the gains
g={g1, ...gL}
for the
L
loud-
speakers of an arrangement from the Ambisonic spectrum yN(θs)
by multiplication with the decoder matrix D:
g=Ddiag{aN}yN(θs).(2)
The matrix is derived from the circular harmonic spectra
yN(θl)
of
each loudspeaker
YN= [yN(θ1),yN(θ2), ..., yN(θL)]
. It can
be calculated by transposition or inversion of
YN
, resulting in a
sampling or mode-matching decoder [
18
], respectively. The energy-
preserving decoder [
19
] uses more sophisticated techniques, such
as singular value decomposition. See the appendix of [
20
] for an
overview about different decoders. In this contribution, the regular
arrangement of
L
loudspeakers (cf. Figure 1) ensures that the simple
sampling decoder is also mode-matching and energy-preserving for
all orders N≤(L −1)/2.
In order to control the main and side lobes emerging from
the truncation of the circular harmonics, a weighting vector
aN
is
applied in the harmonics domain [
17
]. The basic weighting uses a
vector of ones
aN=1
, whereas the max-
rE
weighting suppresses
the side lobes at the cost of a wider main lobe by attenuating higher
orders. This is done by an order-depend weight
a(n) = cos( nπ
2N+2 )
.
Another weighting, called in-phase, yielded no convincing results
in previous experiments [5] and is therefore not used here.
Basically, Ambisonics always uses all available loudspeakers
for the creation of a single phantom source. However, the equiangu-
lar arrangement of
L
even-numbered loudspeakers yields an excep-
tion when using max-
rE
Ambisonics with an order of
N = L/2−1
:
for panning directions exactly in the middle between two neighbor-
ing loudspeakers, only these two loudspeakers are active. In these
cases, max-
rE
Ambisonics yields the same loudspeaker gains as
VBAP and MDAP.
3. EXPERIMENT
The listening experiment evaluates the localization of phantom
sources created by VBAP, MDAP, basic Ambisonics, and max-
rE
Ambisonics at the central listening position.
3.1. Setup and Conditions
All panning methods employ a regular ring of
8
Genelec 8020 loud-
speakers at a radius of
r = 2.5 m
. Figure 1 shows the experimental
setup with additional inactive but visible loudspeakers placed in
5◦
steps in and around the angular range of the target directions.
The height of all loudspeakers was set to
1.2 m
which was also the
ear height of the subjects. The experiment was performed in the
IEM CUBE, a
10.3 m ×12 m ×4.8 m
large room with a mean
reverberation time of
470 ms
that fulfills the recommendation for
surround reproduction in ITU-R BS.1116-1 [
2
,
21
]. The central
listening position lies within the effective critical distance.
The control of the entire experiment and the creation of the
loudspeaker signals used the open source software pure data
1
on a
standard PC with RME audio interface and D/A converters. The
perceived direction was assessed by a pointing method using a
toy-gun that was captured by an infrared tracking system. Details
about the pointing method can be found in [22].
1freely available on http://puredata.info/downloads
42
Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
Both Ambisonics variants use a maximum order of
3
and
MDAP is applied with
B = 10
panning directions uniformly dis-
tributed within a spread of
φMDAP = 22.5◦
. The effect of the
Ambisonics order has already been studied in [
5
] and is not part of
this contribution. All panning methods were evaluated for
9
direc-
tions (with an even spacing of
5.625◦
) between
0◦
and
−45◦
(to
the right). Each of the
36
=
9
(directions)
×4
(panning methods)
conditions was evaluated twice by each subject in random order.
The stimulus consisted of
3
pink noise bursts, each with
100 ms
fade-in,
200 ms
at
65 dB(A)
,
100 ms
fade-out, and
200 ms
silence
before the next fade-in. The stimulus playback could be repeated at
will by the subjects.
There were 14 subjects participating in the experiment. All of
them were part of a trained expert listening panel [23, 24].
3.2. Results
An analysis of variance (ANOVA) showed that the repetition was
not a significant factor (
p= 0.522
for VBAP,
p= 0.465
for
MDAP,
p= 0.085
for basic Ambisonics, and
p= 0.91
for max-
rE
Ambisonics). This confirms a high intra-rater reliability and
thus no subjects were excluded from the results. On the other
hand, the subjects were a highly significant factor (
p0.001
) for
all tested panning methods. This agrees with the inter-subjective
localization found for lateral [
2
] and vertical phantom sources [
25
,
26
]. Nevertheless, the following localization curves summarize all
28 answers from all subjects and repetitions for each condition.
Figure 2 shows the median values and the corresponding
95%
confidence intervals for the
9
different panning angles using VBAP
at the central listening position. Obviously, the panning angle
is a significant factor (
p0.001
). All neighboring conditions
−45 −40 −35 −30 −25 −20 −15 −10 −5 0
−45
−40
−35
−30
−25
−20
−15
−10
−5
0
perceived/predicted angle in °
panning angle in °
Experiment
Ideal
Binaural Model
Intensity Vector
Velocity Vector
Energy Vector
Figure 2: Localization curves for VBAP: experimental results
(median values and
95%
confidence intervals), ideal curve (per-
ceived/predicted angle = panning angle), and predictions by binau-
ral model, intensity vector, velocity vector, and energy vector.
were perceived from significantly different directions (
p0.001
),
except for the angles
−45◦
and
−39.375◦
(
p= 0.053
). In com-
parison to the ideal localization curve (perceived angle = panning
angle), the perceived angles tend towards the loudspeakers. This
tendency is known from [
27
] and is even more distinct for lateral
directions.
Using MDAP, the panning angle is still a significant factor (
p
0.001
). This holds true for the direct comparison of neighboring
panning angles. Compared to VBAP, the median perceived angles
for MDAP are closer to the ideal panning curve and yield a reduced
tendency towards the loudspeakers, cf. Figure 3.
The experimental results for basic Ambisonics show a stretched
trend, i.e. a steeper slope than the ideal curve, cf. Figure 4. The
discriminability of the panning angles is comparable to MDAP.
The significant discriminability of the panning angles holds
true for max-
rE
Ambisonics. Figure 5 shows that the median ex-
perimental results are very close to the ideal localization curve for
this panning method.
Table 1 compares the median deviation of the different panning
methods from the ideal localization curve, i.e., how much the per-
ceived angle deviated from the panning angle. The angles deviate
most for VBAP, in fact more than two times as much as for max-
rE
Ambisonics. The angular match is best for max-
rE
Ambisonics,
followed by MDAP, and basic Ambisonics.
Table 1: Average absolute deviation of median experimental results
from ideal localization curve for different panning methods.
VBAP MDAP basic max-rE
2.35◦1.28◦1.58◦1.05◦
−45 −40 −35 −30 −25 −20 −15 −10 −5 0
−45
−40
−35
−30
−25
−20
−15
−10
−5
0
perceived/predicted angle in °
panning angle in °
Experiment
Ideal
Binaural Model
Intensity Vector
Velocity Vector
Energy Vector
Figure 3: Localization curves for MDAP: experimental results
(median values and
95%
confidence intervals), ideal curve (per-
ceived/predicted angle = panning angle), and predictions by binau-
ral model, intensity vector, velocity vector, and energy vector.
43
Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
−45 −40 −35 −30 −25 −20 −15 −10 −5 0
−45
−40
−35
−30
−25
−20
−15
−10
−5
0
perceived/predicted angle in °
panning angle in °
Experiment
Ideal
Binaural Model
Intensity Vector
Velocity Vector
Energy Vector
Figure 4: Localization curves for basic Ambisonics: experimental
results (median values and
95%
confidence intervals), ideal curve
(perceived/predicted angle = panning angle), and predictions by
binaural model, intensity vector, velocity vector, and energy vector.
Despite this ranking, VBAP yields the smallest standard de-
viations in the experimental results, cf. Table 2. This is mainly
the case for panning angles close to the loudspeakers, which pro-
vide narrow and accurate localization in VBAP in comparison to
phantom sources created by the other methods. Obviously, for
higher number of active loudspeakers, the standard deviation in-
creases. This holds true for the total standard deviation, as well as
for the inter-subjective and the intra-subjective standard deviation.
However, the inter-subjective standard deviation is greater than
its intra-subjective counterpart for all panning methods, agreeing
with the results from the ANOVA that showed the subjects to be a
significant factor, but not the repetition.
Table 2: Mean total, inter-subjective, and intra-subjective standard
deviations of experimental results for different panning methods.
VBAP MDAP basic max-rE
total 2.93◦3.32◦4.61◦4.07◦
inter-subj. 2.52◦2.94◦3.94◦3.54◦
intra-subj. 1.87◦1.90◦2.59◦2.28◦
4. PREDICTIONS
In order to save experiments in the future, it is desirable to find
suitable predictors for the localization of phantom sources. This
section presents a selection of predictors that differ in the measure-
ment effort and it compares their predictions to the experimental
results.
−45 −40 −35 −30 −25 −20 −15 −10 −5 0
−45
−40
−35
−30
−25
−20
−15
−10
−5
0
perceived/predicted angle in °
panning angle in °
Experiment
Ideal
Binaural Model
Intensity Vector
Velocity Vector
Energy Vector
Figure 5: Localization curves for max-
rE
Ambisonics: experimental
results (median values and
95%
confidence intervals), ideal curve
(perceived/predicted angle = panning angle), and predictions by
binaural model, intensity vector, velocity vector, and energy vector.
4.1. Localization Predictors
Binaural Model
This contribution employs a binaural localization model after Lin-
demann [
28
,
29
] which is part of the Auditory Modeling Toolbox
2
.
It divides the binaural input signals into
36
frequency bands with a
spacing of
1ERB
(equivalent rectangular bandwidth) [
30
]. The au-
ditory nerve is modeled by a half-wave rectifier and a low-pass filter
at
800Hz
. In each band, the inter-aural level-difference (ILD) is
considered by monaural detectors and contra-lateral inhibition. The
inter-aural time-difference (ITD) is then computed as the centroid
of the inter-aural cross correlation function [
31
], which delivers one
ITD value for each frequency band.
Within each frequency band, the ITD value of the phantom
source is compared to the values of a single sound source in a lookup
table. The best matching ITD is selected and the corresponding
angle is regarded as the angle of the phantom source for the present
frequency band. A single angle as prediction result is achieved by
the median value of the angles for all frequency bands. The best fit
to the median experimental results has been achieved when using
21
frequency bands covering the range from
164 Hz −3558 Hz
.
On the one hand, the lower frequency limit seems reasonable as
very low frequencies do not yield inter-aural differences because
of the large wavelengths in comparison to the head diameter. On
the other hand, the upper frequency limit underlines the dominant
role of low-frequency ITDs, albeit it also supports the importance
of ITDs at higher frequencies in comparison to the classical duplex
theory [32].
The model is fed with binaural room impulse responses recorded
at the central listening position of the experimental setup with a
2freely available on amtoolbox.sourceforge.net/
44
Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
B&K 4128C dummy head. It uses the first
80 ms
of the impulse
responses. As the model cannot distinguish between front and back,
the ITD values in the lookup table were limited to the directions
between ±45◦, where the conditions of the experiment lie.
Intensity Vector
Sound intensity is a physical measure of the directional sound
power flow and can thus be used to determine the direction where
sound is coming from [
33
]. The intensity
I
is computed from
the scalar sound pressure
p
and the vectorial particle velocity
v
as
I=pv
[
34
]. The sound pressure can be measured by an
omni-directional microphone. The particle velocity is typically
not measured directly but by the pressure gradients
vx
and
vy
using figure-of-eight microphones, each one aligned to the axis
of the coordinate system. Here
p
,
vx
, and
vy
are computed as
the convolution of A-weighted pink noise with impulse responses
measured with two Schoeps CCM 8 figure-of-eight microphones
and an NTI MM2210 omni-directional microphone at the central
listening position.
As a predictor for sound source directions, it is not suitable
to compute the instantaneous direction of the intensity vector for
each sample separately, i.e.
44100
times a second, but rather as a
temporal average within a certain time window. The time window
was set to
80 ms
(
S = 3528
samples), which corresponds to the
binaural localization model. The components
Ix
and
Iy
of the
temporally averaged intensity vector
I=IxIy
are computed as
Ix=
S
X
s=1
p(s)vx(s)and Iy=
S
X
s=1
p(s)vy(s).(3)
The direction of the intensity vector is calculated as
arctan(Iy, Ix)
and is equal to the direction of the velocity vector under free-field
conditions.
Velocity Vector
The direction of the velocity vector was proposed as a simple pre-
dictor for the localization of low frequencies (
≤700 Hz
) [
35
,
36
].
It is calculated as linear summation of the weighted loudspeaker
directions:
rV=PL
l=1 glθl
PL
l=1 gl
.(4)
As it is solely based on the loudspeaker directions and gains, it does
not require any acoustical measurements. It assumes free-field con-
ditions or at least a dominant direct sound. For two loudspeakers,
the velocity vector points towards the same direction as intended
by VBAP.
Energy Vector
Following the idea of the velocity vector, the energy vector
rE
[35, 36] was defined as
rE=PL
l=1 g2
lθl
PL
l=1 g2
l
.(5)
This model assumes an energetic superposition of the loudspeaker
signals and is expected to model the localization direction for higher
frequencies or broadband signals. The magnitude of the energy
vector can also used to describe spatial distribution of energy [
17
]
and the perceived width of phantom sources [37].
4.2. Prediction of the Experimental Results
Along with the experimental results, Figures 2 to 5 show the differ-
ent predictions. Obviously, the direction of the velocity vector is
identical to the desired panning direction for all evaluated panning
methods due to the regular loudspeaker arrangement. For both Am-
bisonics variants, it is also identical to the direction of the energy
vector. The direction of the intensity vector is very close to the
one of the velocity vector. This finding shows that the intensity
vector is the measured counterpart of the velocity vector, even under
non-free-field conditions.
Table 3: Average absolute deviation of predictions from median
experimental results for different panning methods.
VBAP MDAP basic max-rE
Binaural Model 2.35◦3.07◦4.92◦3.37◦
Intensity Vector 2.75◦2.12◦1.89◦2.41◦
Velocity Vector 2.35◦1.28◦1.58◦1.05◦
Energy Vector 1.60◦1.44◦1.58◦1.05◦
Table 3 compares the deviation of the predictions from the
median experimental results. The binaural model yields the worst
prediction, especially for basic Ambisonics. Better results are
achieved by the intensity vector. The vector models yield the
smallest deviations from the experimental results. In detail, the
energy vector predicts the VBAP localization better, as it includes
the effect that the localization tends towards the loudspeakers.
The deviations of the predictions from the experimental results
are similar to the standard deviations of the experimental results.
Thus, all predictors seem to be suitable for the localization of frontal
phantom sources at the central listening position. However, it is
remarkable that the simplest models yield the best predictions at
the same time and the most complex model the worst predictions.
5. CONCLUSION
This contribution investigated frontal phantom source localization
at the central listening position using VBAP, MDAP, basic, and
max-
rE
Ambisonics on a circle of
8
loudspeakers. The match be-
tween the median experimental results and the desired panning
direction was best for max-
rE
Ambisonics and worst for VBAP.
However, the standard deviation of VBAP was the smallest of all
panning methods. Obviously, the standard deviation increases with
the number of active loudspeakers. This is expected to be even
more relevant for off-center listening positions [
2
,
5
,
38
]. The stan-
dard deviation was found to be dominated by the inter-subjective
standard deviation, i.e. the differences between the subjects.
The experimental results were compared to a binaural local-
ization model, the measured intensity vector, and the velocity and
energy vectors. All these predictors seemed to be suitable for the
prediction of the experimental results. It is remarkable that the
velocity and energy vectors as the simplest predictors yielded the
best predictions at the same time. This finding justifies the use of
these predictors in practice. Moreover, there exist first hints that
they can be also applied to vertical or three-dimensional ampli-
tude panning [
39
]. However, their applicability for lateral phantom
sources or off-center listening positions is still under investigation.
45
Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
6. ACKNOWLEDGMENTS
The author thanks all subjects for their participation and the review-
ers for their helpful comments. This work was partly supported
by the projects AAP and ASD, which are funded by Austrian min-
istries BMVIT, BMWFJ, the Styrian Business Promotion Agency
(SFG), and the departments 3 and 14 of the Styrian Government.
The Austrian Research Promotion Agency (FFG) conducted the
funding under the Competence Centers for Excellent Technologies
(COMET, K-Project), a program of the above-mentioned institu-
tions.
7. REFERENCES
[1]
Klaus Wendt, Das Richtungshören bei der Überlagerung
zweier Schallfelder bei Intensitäts- und Laufzeitstereophonie,
Ph.D. thesis, RWTH Aachen, Germany, 1963.
[2]
Matthias Frank, Phantom Sources using Multiple Loudspeak-
ers in the Horizontal Plane, Ph.D. thesis, University of Music
and Performing Arts Graz, Austria, 2013.
[3]
Eric Benjamin, Aaron Heller, and Richard Lee, “Localization
in Horizontal-Only Ambisonic Systems,” in Audio Engineer-
ing Society Convention 121, 10 2006.
[4]
Stéphanie Bertet, Jérôme Daniel, Laëtitia Gros, Etienne
Parizet, and Olivier Warusfel, “Investigation of the Perceived
Spatial Resolution of Higher Order Ambisonics Sound Fields:
A Subjective Evaluation Involving Virtual and Real 3D Mi-
crophones,” in Audio Engineering Society Conference: 30th
International Conference: Intelligent Audio Environments, 3
2007.
[5]
Matthias Frank and Franz Zotter, “Localization experiments
using different 2D Ambisonics decoders,” in 25. Tonmeis-
tertagung, Leipzig, 2008.
[6]
Gavin Kearney, Enda Bates, Frank Boland, and Dermot Fur-
long, “A comparative study of the performance of spatializa-
tion techniques for a distributed audience in a concert hall
environment,” in Audio Engineering Society Conference: 31st
International Conference: New Directions in High Resolution
Audio, 6 2007.
[7] Jens Blauert, Spatial Hearing, MIT Press, 1983.
[8]
David Moore and Jonathan Wakefield, “A design tool to pro-
duce optimized ambisonic decoders,” in Audio Engineering
Society Conference: 40th International Conference: Spatial
Audio: Sense the Sound of Space, 10 2010.
[9]
Ville Pulkki, “Virtual sound source positioning using vector
base amplitude panning,” J. Audio Eng. Soc, vol. 45, no. 6,
pp. 456–466, 1997.
[10]
D. M. Leakey, “Some measurements on the effects of inter-
channel intensity and time differences in two channel sound
systems,” The Journal of the Acoustical Society of America,
vol. 31, no. 7, pp. 977–986, 1959.
[11]
Alan D. Blumlein, “British patent specification 394,325
(improvements in and relating to sound-transmission, sound-
recording and sound-reproducing systems),” J. Audio Eng.
Soc, vol. 6, no. 2, pp. 91–98, 130, 1958.
[12]
Ville Pulkki, Spatial Sound Generation and Perception by Am-
plitude Panning Techniques, Ph.D. thesis, Helsinki University
of Technology, 2001.
[13]
Ville Pulkki, “Uniform spreading of amplitude panned virtual
sources,” in Applications of Signal Processing to Audio and
Acoustics, 1999 IEEE Workshop on, 1999, pp. 187–190.
[14]
Duane H. Cooper and Takeo Shiga, “Discrete-matrix multi-
channel stereo,” Journal of the Audio Engineering Society,
vol. 20, no. 5, pp. 346–360, 1972.
[15]
Michael A. Gerzon, “With-height sound reproduction,” Jour-
nal of the Audio Engineering Society, vol. 21, pp. 2–10, 1973.
[16]
David G. Malham and Anthony Myatt, “3D Sound Spatializa-
tion using Ambisonic Techniques,” Computer Music Journal,
vol. 19, no. 4, pp. 58–70, 1995.
[17]
Jérôme Daniel, Représentation de champs acoustiques, ap-
plication à la transmission et à la reproduction de scénes
sonores complexes dans un contexte multimédia, Ph.D. thesis,
Université Paris 6, 2001.
[18]
Mark A. Poletti, “A Unified Theory of Horizontal Holo-
graphic Sound Systems,” J. Audio Eng. Soc, vol. 48, no. 12,
pp. 1155–1182, 2000.
[19]
Frank Zotter, Hannes Pomberger, and Markus Noisternig,
“Energy-Preserving Ambisonic Decoding,” Acta Acustica
united with Acustica, vol. 98, no. 1, pp. 37–47, 2012.
[20]
Franz Zotter and Matthias Frank, “All-round ambisonic pan-
ning and decoding,” J. Audio Eng. Soc, vol. 60, no. 10, pp.
807–820, 2012.
[21]
ITU, “ITU-R BS.1116-1: Methods for the subjective as-
sessment of small impairments in audio systems including
multichannel sound systems,” 1997.
[22]
Matthias Frank, Ludwig Mohr, Alois Sontacchi, and Franz
Zotter, “Flexible and Intuitive Pointing Method for 3-D Audi-
tory Localization Experiments,” in Audio Engineering Society
Conference: 38th International Conference: Sound Quality
Evaluation, 6 2010.
[23]
Alois Sontacchi, Hannes Pomberger, and Robert Höldrich,
“Recruiting and evaluation process of an expert listening
panel,” in Fortschritte der Akustik, NAG/DAGA, Rotterdam,
2009.
[24]
Matthias Frank and Alois Sontacchi, “Performance review of
an expert listening panel,” in Fortschritte der Akustik, DAGA,
Darmstadt, 2012.
[25]
Ville Pulkki, “Localization of amplitude-panned virtual
sources II: Two- and three-dimensional panning,” J. Audio
Eng. Soc, vol. 49, no. 9, pp. 753–767, 2001.
[26]
Florian Wendt, Matthias Frank, and Franz Zotter, “Applica-
tion of localization models for vertical phantom sources,” in
Fortschritte der Akustik, AIA-DAGA, Meran, 2013.
[27]
Laurent S. R. Simon, Russell Mason, and Francis Rumsey,
“Localization curves for a regularly-spaced octagon loud-
speaker array,” in Audio Engineering Society Convention
127, 10 2009.
[28]
Werner Lindemann, “Extension of a binaural cross-correlation
model by contralateral inhibition. I. Simulation of lateraliza-
tion for stationary signals,” The Journal of the Acoustical
Society of America, vol. 80, no. 6, pp. 1608–1622, 1986.
[29]
Werner Lindemann, “Extension of a binaural cross-correlation
model by contralateral inhibition. II. The law of the first wave
front,” The Journal of the Acoustical Society of America, vol.
80, no. 6, pp. 1623–1630, 1986.
46
Proc. of the EAA Joint Symposium on Auralization and Ambisonics, Berlin, Germany, 3-5 April 2014
[30]
Brian C. J. Moore, Robert W. Peters, and Brian R. Glasberg,
“Auditory filter shapes at low center frequencies,” The Journal
of the Acoustical Society of America, vol. 88, no. 1, pp. 132–
140, 1990.
[31]
Lloyd A. Jeffress, “A place theory of sound localization,”
Journal of comparative and physiological psychology, vol. 41,
no. 1, pp. 35–39, 1948.
[32]
Frederic L. Wightman and Doris J. Kistler, “The dominant
role of low-frequency interaural time differences in sound lo-
calization,” The Journal of the Acoustical Society of America,
vol. 91, no. 3, pp. 1648–1661, 1992.
[33]
Juha Merimaa, “Energetic sound field analysis of stereo and
multichannel loudspeaker reproduction,” in Audio Engineer-
ing Society Convention 123, 10 2007.
[34]
Richard C. Heyser, “Instantaneous intensity,” in Audio Engi-
neering Society Convention 81, 11 1986.
[35]
Y. Makita, “On the directional localization of sound in the
stereophonic sound field,” Tech. Rep., EBU, Review Part A,
73, 1962.
[36]
Michael A. Gerzon, “General metatheory of auditory locali-
sation,” in Audio Engineering Society Convention 92, 3 1992.
[37]
Matthias Frank, “Source width of frontal phantom sources:
Perception, measurement, and modeling,” Archives of Acous-
tics, vol. 38, no. 3, pp. 311–319, September 2013.
[38]
Peter Stitt, Stéphanie Bertet, and Maarten van Walstijn, “Per-
ceptual investigation of image placement with ambisonics
for non-centred listeners,” in DAFx-13, Maynooth, Ireland,
September 2013.
[39]
Florian Wendt, Matthias Frank, and Franz Zotter, “Amplitude
panning with height on 2, 3, and 4 loudspeakers,” in Inter-
national Conference on Spatial Audio, Erlangen, Germany,
2014.
47
