PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Local Ambisonics panning method for creating virtual source in the
median plane
Kailing YI; Bosun XIE1
1

Acoustic lab, School of Physics and Optoelectronics, South China University of Technology, Guangzhou, 510641,
China

ABSTRACTWith the development of multichannel sound with height, it is desired to create virtual source in different
vertical directions, especially in the frontal median plane. For this purpose, a local Ambisonics panning
method is proposed. In a case of analysis, three loudspeakers are arranged in the frontal median plane, with
one locating in the horizontal front and other two locating 30º ~ 45º above or below the horizontal plane,
respectively. The signal amplitudes of loudspeakers are a linear combination of the zero order and first orderharmonics of elevation angle. It is proved that, by properly choosing the weights of linear combination foreach loudspeaker signals, the current method is able to create appropriate interaural time difference as well as
its dynamic variation caused by head rotation and head tilting. Therefore, based on classical Wallach’s
hypothesis and its modern validations, the current method is able to create appropriate dynamic cue forvertical localization in the median plane at low frequency. Results of psychoacoustic experiment indicate thatthe current method yield reasonable localization performance and is superior to traditional pair-wiseamplitude panning. The method can also be extended to create virtual source in other vertical planes.
Keywords: Median plane, Amplitude panning, Dynamic localization cue

1. INTRODUCTION
Some panning methods have long been proposed to recreate virtual source in horizontal surroundsound reproduction. Pair-wise amplitude panning and Ambisonics panning are two familiar panning
methods (1). In the former, signals are fed to two adjacent loudspeakers and virtual source between
loudspeakers are recreated by changing the amplitude ratio of two loudspeaker signals. In the latter,signals are fed to more than three or four loudspeakers around the listener to recreate horizontal virtual
sources. The amplitudes of Ambisonics loudspeaker signals are designed according to azimuthal
harmonics decomposition and each order approximation of target sound field. These panning methods
meet the requirement of the horizontal localization mechanism of human hearing that binaural cues
including ITD (interaural time difference) and ILD (interaural level difference) account for auditory
lateral localization (2). Appropriate loudspeaker configuration and panning methods recreate desired
binaural localization cues and therefore create the perceived of virtual source (summing localization)in various horizontal directions.
With the development of multichannel sound with height (3), it is also desired to recreate virtual
source in different vertical directions, especially in the frontal median plane. Conventional pair-wiseamplitude panning and Ambisonics panning methods have been used or extended to recreate verticalvirtual source. However, the vertical localization mechanism of human hearing differs from that ofhorizontal or lateral localization. Accordingly, the panning methods for creating vertical virtual source
should be examined or even redesigned.
Actually, monaural spectrum at a high frequency caused by the diffraction of head and pinna is awell-known cue for vertical localization (2). However, analysis using head-related transfer functions(HRTFs) and the binaural hearing model indicated that two or more loudspeakers with a conventional
angular interval and panning methods fail to provide correct spectral information for vertical summing
localization (4, 5, 6).
On the other hand, early in 1940, Wallach hypothesized that the ITD variation introduced by head1

Corresponding to: phbsxie@scut.edu.cn

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turning provides dynamic cues for front-back and vertical localization (7). In detail, the ITD variation
caused by head turning around the vertical axis (rotation) allows the discrimination of the front -backlocation as well as vertical displacement from the horizontal plane; and head turning around th e
front-back axis (tilting) provides supplementary information for up-down discrimination. Wallach’sclassical hypothesis has been validated by some modern experiment (8). Jiang et al. further validated
that both high-frequency spectral cue and dynamic cue contribute to vertical localization. However,
the information providing by dynamic and spectral cues is somewhat redundant. When one cue iseliminated, another cue alone still enables vertical localization to some extent (9).
To analyze the summing localization and design the panning method in multichannel sound withheight, some virtual source localization theorems have been proposed. Makita hypothesized that theperceived direction of virtual sources in stereophonic or multichannel sound fields is consis tent with
the normal direction or velocity of the summing wavefront (10). Based on Makita’s hypothesis, Gerzon
proposed a velocity localization theorem or hypothesis for low frequencies below 700 Hz (11). Gerzon
also proposed an energy-localization theorem for high frequency in which the perceived direction of a
reproduced virtual source is supposed to be consistent with the energy flow or sound intensity of thesummed wavefront. Based on Makita’s hypothesis, Pulkki proposed a vector base amplitude panning(VBAP) for multichannel spatial sound which can be regarded as the three dimensional extension of
conventional pair-wise amplitude panning (12).
Based on Wallach’s hypothesis, Xie (XF) derived a set of summing localization equations for
multiple sound sources at low frequency outside the median plane and used them to analyze the spatial
sound reproduction with the 1st-order Ambisonics panning (13). Rao et al. extended those summing
localization equations to the case of median plane (14). By considering aforementioned theorems
comprehensively, Xie et al. developed a framework for analyzing the vertical summing localization ofmultichannel sound reproduction (15).
Xie et al. also proved by analysis and experiment that appropriate two loudspeaker configuration in
the median plane with pair-wise amplitude panning is able to create desired ITD and its dynamic
variation with head rotation, and therefore it is able to recreate virtual source between loudspeakers.
However, the vertical localization information providing by ITD variation with head rotation and headtitling are inconsistent. This inconsistency reduces accuracy in vertical localization (15). In contrast,
the spatial Ambisonics panning is able to create desired ITD and its dynamic variation with headturning. The vertical localization information providing by ITD variation with head rotation and headtitling are consistent. Spatial Ambisonics (especially the 3 order ) yields reasonable vertical
localization performance, but it requires a complicated loudspeaker configuration (15).
Actually, an appropriate vertical panning method should meet the requirement of vertical
localization mechanism of human hearing, and at the same time, be applicable to practical or simple
loudspeaker configuration. For this purpose, a local Ambisonics panning method for recreate thevirtual source in the median plane is proposed in present work.

2. THE LOCAL AMBISONICS PANNING METHOD
Spatial position is specified by spherical coordinates (r, θ, ϕ), where 0 ≤ r < +∞ is the distance; -90°
≤ ϕ ≤ 90° is the elevation and 0° ≤ θ < 360° is the azimuth. ϕ = -90°, 0° and 90° denote the below,
horizontal and above directions, respectively. θ = 0°, 90° and 180° denote the front, left and backdirections, respectively.
As shown in Figure 1, three loudspeakers are arranged up-down symmetrically in the frontal
median plane, with elevations ϕ 0 = -ϕ΄ = -30º ~ -45º, ϕ1 = 0º and ϕ 2 = ϕ΄ = 30º ~ 45º, respectively. For
the 1st order Ambisonics-like panning or signal mixing, the amplitudes or gains of loudspeaker signals
can be expressed as a linear combination of elevation harmonics up to the 1st order:

A0

Atotal (a0  b0 cos IS  c1 sin IS )A1

Atotal (a1  b1 cos IS )A2

Atotal (a0  b0 cos IS  c1 sin IS )(1)

Where ϕS is the target elevation of the virtual source; a0 , a 1, b0 , b 1 and c 1 are a set of coefficients to be
determined; A total is a normalized factor. The up-down symmetry, even function feature of cosϕS and
odd function feature of sinϕS have been considered in Eq. (1). Because signals are fed to only three
local loudspeakers to recreate virtual source in the frontal median plane, this panning method is called5234

“local Ambisonics panning” to distinguish from the conventional (or global) Ambisonics panning inwhich signals are fed to all loudspeakers around the listeners.

Figure 1 – Three loudspeakers configuration for local Ambisonics panning in the frontal median plane
Because all three loudspeakers are arranged in the median plane, the resultant ITD in reproductionis always zeros. Therefore the virtual source locates in the median plane. The coefficient s in Eq. (1) areselected so that the ITD variations caused by head turning in reproduction match with those of target
source at least for low frequency. Based on a shadowless head model (14, 15), a match of ITD variation
caused by head rotation requires:2

cos IS¦ A cos I
i

i

i 0

(2)

2

¦A

i

i 0

A match of ITD variation caused by head tilting requires:2

sin I S

¦ A sin I
i

i

i 0

(3)

2

¦A

i

i 0

Substituting Eq. (1) into Eq. (2) and Eq. (3), a solution of coefficients are given by:

a0 1

a1

2 cos I '

b0

1

b1

2

c

1  cos I 'sin I '

(4)

The normalized factor A total is determined by letting the total power being the unit value:

A02  A12  A23 1(5)

Then the local Ambisonics panning is:

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A1

1  cos I 'sin IS )sin I '
Atotal (2 cos I ' 2 cos IS )A0

Atotal (1  cos IS 

A0

Atotal (1  cos IS (6)

1  cos I 'sin IS )sin I '

With:

Atotal1
1  cos I '2  (1  cos IS )2  2  (sin IS ) 2  4  (cos IS  cos I ') 2
sin I '

(7)

It is worthwhile pointing out that the panning method in Eq. (6) is not only suitable for target virtual
source lies within the region of three loudspeakers, but also suitable fo r target virtual source lies
outside the region of three loudspeakers. In other words, this panning method is theoretically able torecreate vertical virtual source which lies outside the region of three loudspeakers. This is anadvantage of local Ambisonics panning method. Actually, even if the elevation of target virtual sourcelies outside the region of three loudspeakers (ϕ΄ < ϕS ≤ 90º, and -90º ≤ ϕS ≤ -ϕ΄), Eq. (2) and Eq. (3) isstill hold and the local Ambisonics panning still provides correct dynamic cue for vertical localization.
Figure 2 plots the local Ambisonics panning functions of Eq. (6) with the loudspeakerconfiguration being ϕ 2 = ϕ΄ = 45º. When the target direction locates between two adjacent loudspeakers,
the signals for these two loudspeakers are in phase, but the signal for the third loudspeaker is out ofphase. When the target source elevation is consistent with one loudspeaker direction, the signal
amplitudes for other two loudspeakers are zero. When the target virtual source lies outside the regionof three loudspeakers, the signal for the frontal loudspeaker is always out of phase, while the signals
for the other two loudspeakers are always in phase. These are the features of local Ambisonics
panning.

Figure 2 – The local Ambisonics panning functions of Eq. (6) with the loudspeaker configuration being ϕ2 =ϕ΄ =45º.

3. ANALYSIS BY USING HRTFS
Although the analysis in Section 2 indicates that local Ambisonics panning yields appropriate ITD
and its dynamic variation with head turning at low frequency, a more accurate and strict analysis
should take into account the effect of head shadow. This can be realized using HRTFs. For an actual or

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target source at direction (θ S , ϕS ), binaural pressures are calculated as:

PD (T S , IS , f )HD (T S , IS , f ) P0 ( f )(8)Where H α(θ S, ϕ S, f) are a pair of HRTFs with α = L or R representing the left or right ear respectively,
f is frequency. P 0 (f) is the free-field sound pressure at head center with the head absent.
In the case of local Ambisonics panning, the binaural pressures are the linear combination of thosefrom three loudspeakers:

P'D ( f )2

¦ A HD (T ,I , f ) P ( f )
i

i

i

0

(9)

i 0

Where H α(θ i, ϕ i, f) are a pair of HRTFs for i-th loudspeaker at direction (θi , ϕ i), and A0 , A 1, A2 aregiven by Eq. (6). When the head turns, the directions of target source and loudspeakers with respect tohead change. The HRTFs in Eq. (8) and Eq. (9) should be replaced by these of new directions (15, 16).
ITD can be calculated from the resulting binaural pressures. There are various definitions andmethods for ITD calculation (16). Here ITDs are calculated by maximizing the normalized
cross-correlation function between the pressures at two ears. Considering that ITD is a localization cue
at low frequency, the frequency range for calculating the normalized cross-correlation function ischosen up to 1.5 kHz.
The procedures for analysis are:(1). Given the target source direction (θ S, ϕS ), calculate ITD for an actual source and local Ambisonics
panning, respectively. Then compare the results.
(2). Given the target source direction (θ S, ϕ S) and a small azimuth Δθ of head rotation, calculate the ITD
as well as the variation of ITD (ΔITD) for an actual source and local Ambisonics panning,respectively. Then compare the results.
(3). Given the target source direction (θ S, ϕS ) and a small azimuth Δγ of head tilting, repeat step (2).
As an example of analysis, suppose that the elevation of loudspeakers 2 in Figure 1 is ϕ΄ = 45º.
HRTFs of KAEMAR artificial head (with DB-060/061 small pinnae but without torso) are used inanalysis. The HRTFs were obtained by first scanning the images of KAEMAR using a laser scannerand then calculating via BEM-based method (16). The frequency and angular resolutions of HRTFs are
50 Hz and 1º, respectively. The target source elevation ϕ S varies from -90º to 90º at an interval of 5º in
the frontal median plane.
Calculation indicates that, before head turns, the magnitudes of ITD are less than 8 μs for bothactual source and local Ambisonics panning at all target elevations. Therefore, the ITDs created by
local Ambisonics panning match with those of actual source and the virtual sources locate in the
median plane.

(a) The ITD variation (ΔITD) for the actual source(b) The ITD variation (ΔITD) for the actual source

and local Ambisonics panning after head rotationand local Ambisonics panning after head tilting

counterclockwise around the vertical axis with acounterclockwise around the front-back axis with asmall angle Δθ = 15º.

small angle Δγ = 15º.

Figure 3 – The ITD variation (ΔITD) for the actual source and local Ambisonics panning after head rotationand tilting.

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Figure 3(a) plots the ITD variation (ΔITD) for the actual source and local Ambisonics panning afterhead rotation counterclockwise around the vertical axis with a small angle Δθ = 15º. The results for
actual source and local Ambisonics panning are similar. Δ ITD varies with target elevation. It
maximizes at the horizontal front directions ϕS = 0º and reduces as target elevation deviates from thehorizontal plane. Therefore, the ITD variation caused by head rotation provides information forvertical displacement from the horizontal plane. However, this ITD variation is up-down symmetricand does not provide enough information for up-down discrimination.
Figure 3(b) plots the ITD variation (ΔITD) for the actual source and local Ambisonics panning afterhead tilting counterclockwise around the front-back axis with a small angle Δγ = 15º. The results for
actual source and local Ambisonics panning are similar, at least within the range -45 º ≤ ϕ΄ ≤ 45º. ΔITD
also varies with target elevation. It is zeros at the horizontal front directions ϕ S = 0º and opposite at theup and down positions, therefore provides supplementary information for up-down discrimination.
In summary, the results here indicate that local Ambisonics panning method provides consistent
ITD and its dynamic variation with head rotation and tilting for vertical localization in the medianplane. This is consistent with Wallach’s hypothesis.

4. EXPERIMENTAL VALIDATION
A virtual source localization experiment was conducted to validate the local Ambisonics paining
methods. The experiment was carried out in a listening room with reverberation time of 0.15 s. Threeloudspeakers were arranged in an arc with radius 1.45 m, the elevations of three loudspeakers were ϕ0= -45º, ϕ 1 = 0º and ϕ2 = 45º respectively. Subject’s head center was adjusted to consist with the centerof arc.
The elevations of target virtual source ranged from ϕ S = -90º to 90º at an interval of 15º in frontal
median plane. Three kinds of stimuli were used in the experiment, including pink noise with fullaudible bandwidth, low-pass filtered noise with cutoff frequency of 1.5 kHz and orchestral music. The
length of stimuli was 10 s. The sound pressure level in reproduction was about 70 dB. Subjects judged
and reported the perceived directions of virtual source. Head rotation and tilting were encouraged
during the judgment. Eight subjects (five male and three female, with normal hearing) took part in theexperiment. Each subject judged three times. Therefore, there were 3 repetitions × 8 subjects = 24
judgments on each condition. Final results were expressed as the mean perceived azimuth andelevation as well as corresponding standard deviation across 24 judgments. There may be some
up-down (U-D) confusion in the raw localization results. In these cases, the perceived elevation angle
is corrected by reflection against the symmetric plane prior to calculating the mean and standard
deviation. The percentage of confusion is calculated. The percentages of U-D confusion for pink noise,
low-pass filtered noise and orchestral music are 9.0%, 12.5% and 12.5% respectively.

Figure 4 – The mean perceived elevation and standard deviation for three kinds of stimuli.
The mean perceived azimuths lie between -5º to +5º for all three stimuli and target elevations.

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Therefore the perceived virtual source locates near the median plane in all cases. For brief, the figureof mean perceived azimuths is omitted here. Figure 4 plots the mean perceived elevations andcorresponding standard deviations for three stimuli and various target elevations. It shows theperceived virtual source is reasonably consistent with the target source between -60º to +60º for all
three stimuli, and yields consistent with the analysis by using HRTFs in Section 3. Outside the target
elevation of ±60º, the mean perceived elevation is near 60º or -60º.

5. CONCLUSIONSThe local Ambisonics panning method is designed to recreate vertical virtual source by using threeloudspeakers arranged up-down symmetrically in the frontal median plane. It is able to create
appropriate interaural time difference as well as its dynamic variation caused by head rotation andhead tilting, resulting in consistent dynamic cue for vertical localization. This panning method is not
only able to recreate the vertical virtual source within the region of three loudspeakers, but also able torecreate virtual source outside the region of three loudspeakers to some extent. The proposed method
can be extended to recreate virtual source in other vertical plane. This is the future work.

ACKNOWLEDGEMENTS
This work was supported by the National Natural Science Foundation of China (11674105) andState Key Lab of Subtropical Building Science, South China University of Technology.

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