Alois Sontacchi

Markus Noisternig

Robert Holdrich

Thomas Musil

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VECIMS 2003 - lntemafional Symposium nn 
Virtual Environments, Human~Compuler Interfaces, and Measurement Systems 
Lugann, Switzerland, 27-29 July 2003 
3D Binaural Sound Reproduction using a 
Virtual Ambisonic Approach 
Markus Noisternig, Thomas Musil, Alois Sontacchi, Robert Holdrich 
Institute of Electronic Music and Acoustics 
University of Music and Dramatic Arts 
lnffeldgasse 1013, 8010 Graz, Austria 
Phone: +43-316-389-3170, Fax: +43-316-389-3171, Email: noistemig@iem.at 
A- - Convincing binaural sound reprodudion via 
headphones requires fofllfer the virfual sound source signals wifh 
head relafed transfer funcfions (HRTFs). Furfhermore, humnns 
are able lo improve fheir locdimfion capabilifies by smoll 
unconscious head movemenfs. Therefore it is imporfant fa  
incorporate head-tracking. This yields fheproblem of high-quality, 
rime-varying interpolation between dvferent HRTFs A funher 
improvemenf of humnns Iocalizafion accuracy can be done by 
considering room simulafion yielding a huge nmounf of virtual 
sound sources. 
To increase the computafional eflciency offhe proposed sysfem a 
virfual Ambisonic approach is used, fhaf resulfs in a bank offime- 
invarinnf HRTFJXfer independenf of fhe number of sources Io 
encode 
1. INTRODUCTION 
The following paper deals with the theory and practice of 
fully 3D binaural sound reproduction systems using a virtual 
Ambisonic approach. 
Sound source spatializatiou in virtual acoustic 
environments requires to filter the source signals with head 
related transfer functions (HRTFs) to create the left and right 
ear signals. The HRTFs capture the difiaction of a sound 
wave for a certain angle of incidence caused by the torso, 
head, shoulders and pinnae of the listener. Consequently they 
show a great person-to-person variability. Wenzel et al. state 
in [ I ]  that the use of nonindividualized transfer functions 
yields a degradation of humans localization accuracy. In the 
proposed system generic HRTFs have been incorporated 
using the KEMAR [2] as well as the ClPlC database [3]. 
In real-world environments humans are able to improve 
their sound source localization accuracy by performing small 
unconscious head movements [4]. To benefit from this 
phenomenon in binaural sound reproduction systems, head 
tracking has to be taken into account. Furthermore, the use of 
generic HRTFs decreases the perceived externalization of the 
virtual sound source, also termed as out-of-head-localization. 
Begault and Wenzel state in [ 5 ]  that the incorporation of head 
tracking and room simulation improves the localization 
accuracy as well as the perceived extemalization. 
Therefore, the implementation of head tracking and 
moving virtual sound sources yields the problem of high- 
quality time-varying interpolation between different HRTFs. 
To overcome this problem, a virtual Ambisonic approach is 
used that results in a bank of time-invariant HRTF filter. 
Ambisonic is a sound reproduction technique involving a 
limited number of playback channels, while allowing 
reproduction of a full three dimensional acoustic space with 
several moving virtual sources. 
The following section gives a brief introduction into 
Ambisonic theory. In section Ill a binaural sound 
reproduction system is developed using the Ambisonic 
approach, incorporating head tracking as well as room 
simulation. 
11. THE AMBlSONlC APPROACH 
Ambisonic is a technique for spatial audio reproduction 
introduced in the early seventies by Gerzon [6]. Further 
details of Ambisonic theory are published in [7] - [ I  I]. 
The holographic theory of wave field reproduction states 
that the Kirchhoff - Helmholtz integral relates the pressure 
inside a source free volume of space to the pressure and 
velocity on the boundary at the surface. Recently it has been 
shown that the Ambisonic formulation is asymptotically 
holographic assuming plane wave loudspeaker signals [7], 
[8]. Deriving the Ambisonic coding and decoding equations 
from the Kirchhoff - Helmholtz integral it can be shown, that 
the original wave field may be reconstructed exactly by 
arranging infinitely many loudspeakers on a closed contour. 
Using a finite number of N loudspeakers arranged on a sphere 
a good approximation of the original sound field may be 
synthesized over a finite area (sweet spot). In [9] it is shown, 
that higher order Ambisonic systems are increasingly 
accurate. 
The decomposition of the incoming wave field into 
spherical harmonics can be shown deriving Ambisonic from 
the homogenous wave equation 
i a  
Ap(t, r) - -- p(t, r) = 0 
cs h2 
where p(t,r) is the sound pressure at the position r and c 
is the speed of sound. Solving the wave equation for the 
incoming sound wave as well as for the plane waves of the 
several loudspeakers yields the so called matching conditions 
[I01 
0-7803-7785-0/03/$17.00 02003 IEEE 
174 
N 
s .  Y,,(Q,@) = C P "  .X.,(YJ", 9) (2) 
"=I 
The left side of (2) represents the Ambisonic encoding 
equation, 
B 0 . B  = Y 0 . d  (3) 
where Bo,@ represents the Ambisonic channels in vector 
notation, s is the pressure of the original sound wave coming 
from direction (Q,O) and YR.; describes the spherical 
harmonics. On the right hand side of (2) p. is the signal of the 
nth loudspeaker at direction (vn,Sn). The spherical 
harmonics can be calculated as follows 
A,,vP,"(cosO)cos(m@) f o r o =  1 
Am,qP,"(cos@)sin(mQ) fo ro=- I  (4) 
where P," represents Legendre polynomials. Now, using 
vector notation (2) may be written as 
B = C . p  (5) 
where 
P = [PI .P2> . . . PN I' 
is the loudspeaker signal vector and 
B = [U&(@, 0), Y;,,,(@, 0), . . . Y& (@, O)]' s (7) 
represents the Ambisonic channels. The Matrix C contains 
'the decomposition of the several loudspeaker signals using 
spherical harmonics. 
Now it is possible to calculate the decoding from the 
encoding equations as follows 
D = pinv(C) = CT . (C . CT)-' (8) 
As can be seen, the decoding stage will only depend on the 
actual loudspeaker amngement. Consider the reproduction of 
a 2D field using a finite number of  loudspeakers and deriving 
the horizontal holographic approach 6om the two 
dimensional spatial Fourier transform it is shown in [9], [ I  I], 
that the decoding process may be described by the so called 
angular sinc functions (asincs). Consider the asinc-functions 
it can be seen that the auditory localization may be confused 
by signals coming from loudspeakers far away from the 
intended position of the virtual sound source. Like in 
conventional signal processing techniques using the Fourier 
transform, windowing can be used to attenuate the sidelobes 
of the asinc functions. Weighting the amplitudes of higher 
order Ambisonic channels is used to attenuate far away 
speaker signals considering just noticeable difference 
thresholds (JND) to increase localization accuracy. A 
broadening of the main lobe will occur as well yielding a 
broadening of the perceived sound source increasing the 
localization blur. 
111. DEVELOPMENT OF A BINAURAL SYSTEM 
Incorporating head tracking and moving virtual sound 
sources in binaural sound reproduction systems, the 
conventional approach of spatialization by convolving the 
source signals with HRTFs yields the problem of time- 
varying interpolation between different HRTFs. This 
interpolation results in  ifa acts decreasing the localization 
performance of the system. As mentioned above, to overcome 
the problem of time-varying interpolation between different 
HRTFs a virtual Ambisonic approach is used, as described in 
the following section. 
A. The virtual Ambisonic approach 
The virtual Ambisonic approach is based on the idea to 
decode Ambisonic to virtual loudspeakers. Then, after 
decoding the binaural signals are created by convolving the 
virtual loudspeaker signals with HRTFs appropriate to the 
loudspeaker position in space. Now the filtered signals are 
superimposed to create the left and right ear headphone 
signals (figure I ) .  
Figure 1. Block diagram of the 3D binaural sound reproduction 
system incorporating head tracking as well as room simulation. 
I75 
A review of literature states that the Ambisonic approach 
offers a good localization performance only over a small 
listening area (sweet spot). However, binaural sound 
reproduction does not suffer from this effect, because due to 
the headphones the listeners position is always in the sweet 
spot area. 
Moreover, the virtual sound source signals are encoded 
into Ambisonic domain dependent to their position in virtual 
space. To embrace their variable distances, the sound source 
signals are delayed relative to the listeners position first. 
Furthermore, the high frequency damping due to the sound 
waves propagation path is taken into account by simple IIR 
low-pass filter. Using fully 3D Ambisonic of MIh order yields 
(M+1)2 transmit channels independent of the number of 
sources to encode. As shown later, this fact is important for 
room simulation. Henceforth, head rotation is taken into 
account by simple rotation matrices in the Ambisonic 
domain. Head rotation is identified by the use of a head 
tracking device mounted on the headphones. 
As mentioned above, the decoder is defined solely by the 
position of the virtual loudspeakers. To avoid ill conditioning 
or singularities in the decoder matrix, it is important to 
distribute the virtual loudspeakers as uniformly as possible 
over the spheres surface. 
Filtering with HRTFs is a highly computational task. 
Listening tests and error analysis of a 2D system have shown 
that shorten HRTFs up to 128 points yields a satisfactory 
localization accuracy [13], [I41 (figure 2). Furthermore the 
use of individualized HRTFs will increase localization 
capabilities. Further investigations on the influence of 
different HRTFs to the overall systems localization 
performance have not been carried out during this work. 
B. Room Simulation 
To improve the perceived externalization of a virtual 
sound source the incorporation of room simulation is an 
important fact for binaural sound reproduction. In this section 
we focus on the simulation of sound reverberation as a 
natural phenomenon occurring when sound waves propagate 
in an enclosed space. The calculation of the room simulation 
is divided into two stages. First, the early reflections of fust 
and second order are calculated. Then a model for efficient 
simulation of the diffuse sound field is introduced. 
The early reflections are taken into account using a simple 
geometrical acoustic approach by calculating image sources. 
We are considering a rectangular room containing omni- 
directional vimal point sources. To consider the acoustic 
properties of the reflecting walls, the image source signals are 
filtered with a low order IIR low-pass filter. According the 
different distance of the image sources to the listening 
position, the image source signals are delayed and attenuated 
as well. Then every image source is encoded to Ambisonic 
dependent to their position in the virtual acoustic space. 
Due to the fact, that higher order early reflections become 
more and more diffuse they are encoded with lower order 
Ambisonic. The loss of localization accuracy may be 
accepted to increase the computational efficiency. 
Another approach to decrease computational cost for 
encoding the image sources is to divide the virtual space into 
several subspaces or regions of influence. Now image sources 
situated in same subspaces are bundled and encoded to 
Ambisonic domain according to the direction dedicated to 
their respective subspace. 
1: 1; 
2 0  itd 
I rdh.&.ke 
Figure 2. Localization error in degrees for binaural sound 
reproduction systems using different HRTFs (1.2) and different 
interpolation techniques (AB) 
Late reverberation creates an ambient space in the 
perception of the listener. A computational efficient 
calculation is to implement reverberators with all-pass 
circuits embedded within very large globally recursive 
networks (figure 3). To handle the stan time of late 
reverberation the input signal is delayed. Then the signal is 
low-pass filtered to consider the coloration due to the 
absorption of high frequency signal components at the 
enclosing walls. 
Figure 3. Recursive reverberation nemo* 
176 
The first set of input diffusers is used to quickly 
decorrelate the incoming signal to prepare it for the next stage 
of computation. To loop the decorrelated sound indefinitely 
the second diffuser stages are arranged to feed back globally 
on themselves. By multiplying a gain factor 4.0 in the 
feedback paths it is possible to control the decay time. The 
low-pass filter in the feedback paths incorporates the texture 
of materials at the enclosing walls as before. 
Finally the reverberation signals are encoded into 
Ambisonic domain. Because of the fact that reverberation 
signals do not affect localization accuracy, low order 
Ambisonic is sufficient for encoding. 
Incorporating this reverberation network yields a simple 
way to control parameters of the reverberated sound like 
diffusion of the input and decay signals 
(decurrelation) 
reverberation pre delay 
reverberation gain 
decay rate 
C. Optimization 
cut-off frequency of the high frequency damping 
To increase the computationally efficiency of the overall 
system, the following improvements have been carried out: 
Using shorter HRTF-filter increases the computational 
efficiency. Further studies and listening tests have shown 
[13], [I41 that a filter length less then 128 taps yields a 
satisfactory localization performance. 
Moreover, the use of a mixed order Ambisonic setup 
reduces the computational cost of the encoding as well as of 
the decoding stage. Because of the fact that humans 
localization accuracy is much more better in horizontal than 
in vertical directions, it is possible to encode elevation cues 
with Ambisonic of lower order. 
The possibilities to reduce the computational cost of room 
simulations using lower order Ambisonic for encoding higher 
order reflections as well as bundling the image source signals 
according to their direction in virtual space are described in 
the previous section. 
IV. IMPLEMENTATION 
First a 2D system using 4’ order Ambisonic was 
implemented on a digital signal processor (DSP) running a 
PC as a host system. The system has been optimized using 
the mathematical model described in [13]. Furthermore the 
mathematical model as well as the systems localization 
accuracy has been evaluated by listening tests, using the 2D 
DSP platform to render the binaural signals in real-time [14]. 
The incorporation of the abovementioned optimizations 
made it possible to implement a fully 3D system with 
Ambisonic of 4’ order on a usual notebook running a 
I.6GHz CPU. The proposed system was programmed using 
Pure Data (PD). PD is a graphically based open source real 
time computer music software by Miller Puckette [ 151. 
V. CONCLUSIONS 
In this paper the advantages of using the virtual Ambisonic 
approach to cany out binaural sound reproduction in real- 
time has been discussed. For multiple moving sound sources 
this approach brings an enormous benefit in increasing the 
computational efficiency of the system. The main advantages 
are 
Rendering the sound field using Ambisonic in time- 
variant binaural sound reproduction systems yields 
time-invariant HRTFs without the need of 
interpolation between them. 
The number of HRTFs is independent of the number 
of virtual sound sources to encode. This is quite 
important because incorporating room simulation by 
calculating early reflections of first and second order 
yields an enormous increase of virtual sound sources 
to encode. 
Ambisonic provides a decoupling of the encoder and 
decoder. Hence, the awareness of the playback 
configuration can be limited to the decoder while 
only the universal multi channel format is 
implemented in the encoding stage. 
Head rotation may be taken into account with simple 
time-variant rotation matrices using a head tracker 
mounted on the headphones. 
With the rapid increase of CPU power it will become 
possible to run multi channel binaural sound reproduction 
systems as background tasks for applications like plug-ins for 
computer music software and for example interactive 
acoustical interfaces for blind persons. 
As future research, a comprehensive localization error 
analysis of the proposed system would be interesting using 
the objective mathematical model of localization as well as 
listening tests. 
VI. ACKNOWLEDGEMENT 
This work was partially supported by AKG-Acoustics 
GmbH, Vienna, Austria and the author wishes to thank 
Martin Opitz and Stefan Leitner for inspiring discussions. 
VII. REFERENCES 
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178 


3D Binaural Sound Reproduction using a Virtual Ambisonic Approach

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3D Binaural Sound Reproduction using a Virtual Ambisonic Approach

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