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

The limitation of static transaural reproduction
with two frontal loudspeakers
Lulu LIU1; Bosun XIE2
1

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

2

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

ABSTRACT
Incorporated HRTF-based binaural synthesis and cross-talk cancellation, transaural reproduction with two
frontal loudspeakers is theoretically able to duplicate the binaural pressures of an actual sound source, andthen is expected to be able to recreate virtual source at arbitrary direction. However, many experiments haveindicated that for static transaural reproduction, in which transaural processing is fixed regardless of headturning, the perceived virtual source is usually limited in the frontal-horizontal plane. The reason may be that,in static transaural reproduction, the dynamic cue for front-back and vertical localization is omitted, while thehigh-frequency spectral cue is unstable against head movement. To validate this hypothesis, a psychoacoustic
experiment is conducted in present work. A dynamic transaural system with two frontal loudspeakers is usedin the experiment. According to the contemporary orientation of head detected by a head-tracker, the systemchanges the transaural processing so that binaural pressures in reproduction follow the turning of subject’s
head. The experimental results indicate that, by incorporating the dynamic cue caused by head turning,dynamic tranaural reproduction is able to recreate virtual source at front, back and vertical directions.
Therefore, the limitation in conventional static transaural reproduction is indeed caused by the omitting ofdynamic cue.
Keywords: Transaural reproduction, Vertical localization, Dynamic cue

1. INTRODUCTION
Binaural pressures include the main information for auditory localization. Based on HRTF-based
binaural synthesis, binaural reproduction or virtual auditory display (VAD) duplicate s the binauralpressures caused by an actual sound source and then recreates perception of virtual source localizationin three dimensional space through headphone reproduction (1).
Incorporated HRTF-based binaural synthesis and cross-talk cancellation, transaural reproduction
with two frontal loudspeakers is theoretically able to duplicate the binaural pressures of an actual
sound source, and then is expected to be able to recreate virtual source at arbitrary direction. Someauthors reported that, under a series of critical conditions (e.g., individualized HRTF processing,
restriction of head movement, reproduction in anechoic rooms, etc.), a pair of frontal loudspeakers canrecreate perceived virtual sources at all horizontal or three -dimensional directions for listeners, tosome extent (2). However, more experimental results indicate that, in static transaural reproductions(especially these with nonindividualized HRTF processing), perceived virtual source positions areusually limited in the region of frontal-horizontal quadrants (3). The virtual sources intended forrear-horizontal quadrants or high elevations are often perceived at the frontal-horizontal quadrants
with the same cone of confusion.
Actually, in the case of an actual sound source, both high-frequency spectral cue included inbinaural pressures and dynamic variation of binaural pressures caused by head turning contribute to
front-back and vertical localization (4,5). In static transaural reproduction, the transaural processing isfixed regardless of head turning and therefore the dynamic cue is omitted or unmatched. Moreover, thehigh-frequency spectral cue in loudspeaker reproduction is unstable against head movement due to theshort wavelength. Therefore, it is reasonable to hypothesize or deduce that the aforementioned
1
2

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348802659@qq.com
Corresponding to: phbsxie@scut.edu.cn

limitation in static transaural reproduction with two front loudspeakers is ca used by the unmatched
dynamic cue and unstable high-frequency spectral cue. To test this hypothesis, the dynamic variationof interaural time difference (ITD) caused by head turning in transaural reproduction is analyzed inpresent work. Virtual source localization experiments for both static and dynamic transaural
reproductions through two frontal loudspeakers are conducted. The analysis and experimental results
validate the hypothesis.

2. PRINCIPLE OF TRANSAURAL REPRODUCTION
There are various methods to derive the loudspeaker signals for transaural reproduction with two
frontal loudspeakers in the horizontal plane. The conventional method is to cascade the HRTF -based
binaural synthesis and cross-talk processing (6). Here, an alternative but mathematically equivalentmethod is outlined (7).
For convenience in analyzing vertical or elevation localization, the interaural polar coordinate isused in the present work. The origin of coordinate is located at the center of the head. Source positionis specified by (r, Θ, Ф). Where 0 ≤ r < ∞ denotes the source distance; -90º ≤ Θ ≤ 90º denotes theinteraural polar azimuth, that is, the angle between the directional vector of the sound source and the
median plane, with Θ = -90º, 0º, and 90º being the left direction, median plane, and right direction,
respectively. A constant Θ represents the cone of confusion. The -90º ≤ Ф < 270º denotes the interauralpolar elevation, that is, the angle between the projection of the directional vector of the source to themedian plane and the frontal axis, with Ф = -90º, 0º, 90º, and 180º being the below, front, above, andback directions, respectively.
For an actual or target virtual source at far-field distance (r ≥ 1.2 m) and direction (Θ S, Ф S), thebinaural pressures in the frequency domain can be calculated by filtering the input stimulus E(f) witha pair of corresponding HRTFs H L (ΘS, ФS , f) and H R (Θ S, ФS , f):ª PL º ª H L (ΘS , ΦS , f ) º(1)« P » « H (Θ , Φ , f ) » E ( f )¬ R¼ ¬ R S S¼
For transaural reproduction with two frontal loudspeakers, two loudspeakers are arranged at far-field
distance (r ≥ 1.2 m) and directions (ΘL , Ф L = 0Ϩ), (Θ R, Ф R = 0Ϩ) respectively. Let E L (f) and E R(f) be theloudspeaker signals, H LL(ΘL , Ф L, f), H RL (Θ L, ФL , f), HLR (Θ R, Ф R, f) and H RR(Θ R, Ф R, f) denote the four
acoustic transfer functions from two loudspeakers to two ears. The reproduced binaural soundpressures at the two ears are given by:ª P 'L º ª H LL (ΘL , ΦL , f ) H LR (ΘR , ΦR , f ) º ª EL ( f ) º(2)« P ' » « H (Θ , Φ , f ) H (Θ , Φ , f ) » « E ( f ) »¬ R ¼ ¬ RL L L
¼¬ R
¼
RR
R
R
Letting Eq (2) be equal to Eq.(1), that is, the binaural pressures in transaural reproduction be equal
to those of target, the loudspeaker signals can be found as:
E 'L (ΘS , ΦS , f ) GL (ΘS , ΦS , f ) E ( f )E 'R (ΘS , ΦS , f ) GR (ΘS , ΦS , f ) E ( f )(3)
Where G L(Θ S, Φ S, f) and G R(Θ S, Φ S, f) are the responses of a pair transaural filters which depend on
directions of target source and loudspeakers with respective to head.
H RR (ΘR , ΦR , f ) H L (ΘS , ФS , f )  H LR (ΘR , ΦR , f ) H R (ΘS , ФS , f )GL (ΘS ,ФS , f )H LL (ΘL , ΦL , f ) H RR (ΘR , ΦR , f )  H LR (ΘR , ΦR , f ) H RL (ΘL , ΦL , f )(4)
 H RL (ΘL , ΦL , f ) H L (ΘS , ФS , f )  H LL (ΘL , ΦL , f ) H R (ΘS , ФS , f )GR (ΘS ,ФS , f )H LL (ΘL , ΦL , f ) H RR (ΘR , ΦR , f )  H LR (ΘR , ΦR , f ) H RL (ΘL , ΦL , f )Therefore, by filtering the input stimulus with a pair of transaural filters, transaural reproduction isable to control the binaural pressures caused by two loudspeakers so that they are equal to those causedby an actual source. This is the basic principle of transaural reproduction with two front loudspeakers.
In practical uses, appropriate equalization algorithm may be supplemented to the transauralsynthesis to reduce the perceived timbre coloration in reproduction. The timbre equalization is basedon the fact that in two frontal loudspeaker reproduction, the perceived virtual source direction isdominated by interaural cues (especially ITD) and is limited to frontal -horizontal quadrants. Theinteraural cues are controlled by the relative, rather than the absolute, magnitude and phase of left andright loudspeaker signals. Scaling both loudspeaker signals with identical frequency -dependent
coefficients does not alter their relative magnitude and phase, or the perceived virtual source azimuth.
However, this manipulation alters the overall power spectra of loudspeaker signals and therefore

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equalizes timbre. Of course, equalization algorithms may alter the spectra of binaural pressures. For
constant-power equalization algorithms (1), the responses of the transaural synthesis filters areequalized by their root mean square (RMS). That is, the GL(ΘS, ΦS, f) and GR(ΘS, ΦS, f) in Eq.(4) aresubstituted by the following G’ L (ΘS, ΦS , f) and G’ R(ΘS , ΦS , f):
GL (ΘS , ΦS , f )G 'L (ΘS , ΦS , f )| GL (ΘS , ΦS , f ) |2  | GR (ΘS , ΦS , f ) |2
(5)
GR (ΘS , ΦS , f )G 'R (ΘS , ΦS , f )| GL (ΘS , ΦS , f ) |2  | GR (ΘS , ΦS , f ) |2
After equalization, the loudspeaker signals given by Eq.(3) and Eq.(5) satisfy the constant-power
spectral relationship,(6)| E 'L (ΘS , ΦS , f ) |2  | E 'R (ΘS , ΦS , f ) |2 | E( f ) |2
Therefore, the overall power spectra of loudspeaker signals are equal to those of the input stimulus,
thereby reducing reproduction coloration.
When subject’s head turns, the HRTFs from target source and two loudspeakers to two ears change.
In dynamic transaural reproduction, the head turning is detected by a head tracker. Accordi ng to thedirection of the target virtual source relative to the temporary orientation of the subject’s head, the
HRTFs in the two transaural filters of Eq.(4) or (5) are updated constantly. The detail of dynamictransaural reproduction is referred to (3,8).

3. ANALYSIS ON DYNAMIC LOCALIZATION CUE
To analyze dynamic localization cue, the ITD (interaural time difference) vari ation caused by headturning in transaural reproduction is analyzed and compared with that of an actual source.
For an actual source at direction (ΘS , ФS ), the binaural pressures are evaluated by Eq.(1). When thehead turns, the binaural pressures are also evaluated by Eq.(1), but the HRTFs at new direction withrespect to head are used.
For static transaural reproduction, the binaural pressures are evaluated by Eq.(2) with theloudspeaker signals given by Eq.(3) and (4) in the case without timbre equalization, or given by Eq.(3)and (5) in the case with timbre equalization. When the head turns, the HRTFs from the two
loudspeakers to two ears should be replaced by those at new directions with respect to head, but theloudspeakers signals are unchanged.
For dynamic transaural reproduction, the binaural pressures are evaluated similar to static
reproduction. But when the head turns, both the HRTFs from the two loudspeakers to two ears and theloudspeakers signals should be changed according to the new directions with respec t to head.
Subject’s head is able to turn in three degrees of freedom, including turning around the left -rightaxes (pitch), around the front-back axes (tilting or rolling), and around the up-down axes (rotation oryaw). The ITD variation caused by head rotation is supposed to provide information for front-back andvertical localization, and the ITD variation caused by head tilting also provides supplementary
information for up-down discrimination (5,9,10). Therefore, the ITD variations caused by headrotation and titling are evaluated.
There are various definitions and methods for ITD calculation(1). Here, the ITDs are calculated by
maximizing the normalized cross-correlation function between the pressures at the two ears.
Considering ITD is an effective localization cue at low frequency, the frequency range for the ITD
calculation is chosen up to 1.5 kHz.
The schemes for analysis are as follow.
1) Calculate the binaural pressures for an actual source before and after head turning, respectively.
2) Calculate the ITD for an actual source before and after the head turning, respectively, and then,evaluate the variation in ITD.
3) Calculate the binaural pressures for transaural reproduction before and after head turning,respectively.
4) Calculate the ITD for transaural reproduction before and after head turning, respectively, andthen, evaluate the variation in ITD.
5) Compare the ITD variations for actual source and transaural reproduction.
As an example of analysis, suppose that two loudspeakers are arranged in the horizontal plane. The
distance between the loudspeakers and the head center of subject is 1.5m, and the directions are:5242

ΘL 15q
ΘR 15qΦL ΦR 0q
(7)
The actual or target source is located in the median plane. HRTFs of KAEMAR artificial head (withDB-060/061 small pinnae but without torso) are used in analysis. The HRTFs were obtained by firstscanning the images of KAEMAR using a laser scanner and then calculating via the fast boundary
element method (11). The sample frequency of HRTFs is 44.1 kHz and the length is 512 points.
Figure 1 shows the ITD variation (ΔITD) for various actual or target source polar elevations in the
median plane and head rotation to the left with an azimuth of 10°. The results for actual source, staticand dynamic transaural reproduction with timbre equalization are plotted in the same figure. The
results of static and dynamic transaural reproduction without timbre equalization are almost identicalto those with timbre equalization and therefore omitted here.

ITD variation/μs

100
50
0
-50
-100
-30

actual source
staticdynamic

0 30 60 90 120 150 180 210
Target polar elevation Фs / degree

Figure 1 –Results of ITD variation for target source polar elevationsin the median plane and head rotation to the left with an azimuth of 10°
In all cases, as expected, the ITD ≈ 0. In the case of actual source, the ΔITD varies with elevation.
In the frontal-median plane -30º ≤ ФS < 90º, ΔITD > 0; and in the back-median plane, ΔITD < 0.
Therefore, the sign of ΔITD provides information for front-back discrimination. In addition, themagnitude of ΔITD maximizes in the horizontal-frontal and back direction. As the source elevation
departs from the horizontal plane, the magnitude of ΔITD is reduced. At the top with ФS = 90° (orbottom with Ф S = -90°, not shown in the figure), the ΔITD is zero. Therefore, the ΔITD with headrotation provides information for vertical displacement from the horizontal plane. However, the ΔITD
with head rotation is up-down symmetric. For example, the ΔITD for Ф S = 30º and -30º are almost
identical. In fact, the ITD variation caused by head tilting (as well as scattering by torso) provides
further information for up-down discrimination.
In the case of static transaural reproduction, the ΔITD with head rotation are almost invariant
against target elevation (96 μs to 97μs) and basically consistent with that of actual source near thefront ФS = 0º. While in the case of dynamic transaural reproduction, the ΔITD with head rotation arealmost consistent with that of the actual source at various elevations.
It can be proved that for head rotation with other small azimuth (for example, 20°) or for headtilting, the ITD variation exhibit a similar feather. That is, in the case of static transaural reproduction,
the ITD variations with head turning are basically identical to that of actual source near the front. And
in the case of dynamic transaural reproduction, the ITD variations with head turning basically matchwith those of actual source at target directions.

4. EXPERIMENT METHOD
A series of virtual source localization experiments were conducted to examine the perceived virtual
direction of static and dynamic transaural reproduction.
The experiment was conducted in a listening room with reverberation time of 0.15 s. Static anddynamic transaural reproduction with timbre equalization were examined. Two loudspeakers(GENELEC 8010AP-5) were arranged in the horizontal plane at a distance of 1.5 m and azimuths
given by Eq.(7). Nine target elevations from ФS = -30º to 210º at an interval of 30º in the median plane
were chosen. The HRTFs used in transaural synthesis were identical to those in Sec.3. Two kinds ofstimuli, pink noise with full audible bandwidth and 3 kHz low-pass pink noise, were used. The lengthof stimuli was 10 s.

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In dynamic reproduction, an electromagnetic head tracker (Polhemus FASTRAK) was used todetect the orientation of the subject’s head. It was able to detect the head turning in three degrees of
freedom. The update rate and system latency time of the dynamic reproduction were 60 Hz and 25.4 ms,
respectively.
The subjects judged the perceived virtual source direction and reported using an electromagnetic
tracker (Polhemus FASTRAK). The tracker included two receivers. One receiver was fixed on thesubject’s head surface to monitor the position and orientation of the head. Another receiver was fixedat one end of a 1.0 m wooden rod. The subject pointed the rod at the position of the perceived virtual
source and a computer recorded the result. The direction of the virtual source was measured relative tothe head center because the data relative to the receiver on the head surface had been transferred tothose relative to the head center. The subjects made the judgment and pointed at the perceived
direction during the stimulus presentation. Before and after a presentation, the subjects were allowed
to turn their heads to recognize the direction.
For static reproduction, the subject’s heads were restricted during the judgment. The data from thehead tracker indicated that the angle of head rotation and titling are less than 2º, respectively. For
dynamic reproduction, the subjects were encouraged to turn their heads. For dynamic reproduction, theangle of head rotation ranged from ±5º to ±15º; and the angle of head titling ranged from ±10º to ±25º.
Eight subjects participated in the experiment. The subjects were from 22 to 30 years old and hadnormal hearing. Under each condition and at each target direction, each subject repeatedly judged
three times. Therefore, there were 3 repetitions × 8 subjects = 24 judgments under each condition.
Statistical analysis was applied to the 24 judgments.

5. RESULTS AND STATISTICS
The preliminary results from the subjects indicated that, for static reproduction with stimuli of two
bandwidths and for dynamic reproduction with 3 kHz low-pass pink noise, a single virtual source wasperceived. In this case, statistical analysis was applied to the perceived directions of this virtual source.
However, for dynamic reproduction with pink noise of full audible bandwidth, two splitting virtual
source were perceived. The high-frequency one was always perceived at the horizontal frontal
directions. The low-frequency one was perceived at different elevation in the median plane, dependingon the target elevation. In this case, statistical analysis was only applied to the perceived directions of
the low-frequency virtual source.
Although the localization results varied across the subjects, the overall tendency was similar. The
perceived virtual source was located near the median plane with mean unassigned polar azimuth errors
being less than 2.6º in all cases. For brevity, only the statistical results of all the subjects are analy zed
here. Figure 2 show the mean polar elevation and corresponding standard deviation. Reversal was
resolved for the raw localization results with front-back (F-B) and up-down (U-D) confusions. Table 1
lists the percentage of confusion.
Table 1 –Percentage of confusion for each target virtual source reproduction
Dynamic

Full band
Low-pass

StaticFull band
Low-pass

-30

0

30

60

90

120

150

180

210

F-B confusion(%)

0

0

4.2

25

/

29.1

8.3

8.3

8.3

U-D confusion(%)

70.8

/

4.2

4.2

8.3

4.2

8.3

/

70.8

F-B confusion(%)

0

0

0

16.7

/

16.7

8.3

8.3

12.5

U-D confusion(%)

79.1

/

4.2

0

0

0

4.2

/

75

F-B confusion(%)

0

0

0

0

/

100

100

100

100

U-D confusion(%)

/

/

/

/

/

/

/

/

/

F-B confusion(%)

0

0

0

0

/

100

100

100

100

U-D confusion(%)

/

/

/

/

/

/

/

/

/

Figure 2(a) shows the results of static reproduction. The results for the stimuli with two different
bandwidths are similar. For target source at the front median plane and top direction with -30º≤ Φ S ≤90º, the mean perceived directions are near the Φ I = 0º, and Table 1 indicate that no front-backconfusion occurs. For target source at the back median plane with 12 0º ≤ ΦS ≤ 210º , Figure 2(a)indicates the mean perceived directions are near the Φ I = 180º. However, Table 1 indicates the

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240
210
180
150
120
90
60
30
0
-30
-30

full
low

0 30 60 90 120 150 180 210
Target polar elevations Фs / degree

perceived polar elevations/degrees

perceived polar elevations/degrees

percentage of front-back confusions are 100 %. Therefore, for target source at -30º ≤ Φ S ≤ 210º, theactual perceived directions are all at the horizontal front, in spite of the target directions.
Figure 2(b) shows the results of dynamic reproduction. The results for 3 kHz low -pass pink noise
and the low-frequency virtual source of pink noise with full-audible bandwidth are similar. The mean
perceived elevations basically match with the target ones. Table 1 indicates that no or low front-backconfusion occurs in most cases, except for some front-back confusions occur at the target directions Φ S= 60º and 120º. In addition, only a few up-down confusions occur, expect for the low-elevation target
directions of Φ S = -30º and 210º at which the percentages of up-down confusion reach high values of
70.8 % ~ 89.1 %.
240
210
180
150
120
90
60
30
0
-30
-30

full
low

0 30 60 90 120 150 180 210
Target polar elevations Фs / degree(a) Static reproduction(b) Dynamic reproduction
Figure 2 – Mean results and standard deviation of virtual source
polar elevation localization in the median plane

6. DSICUSSION
The experimental results in sec.5 indicate that static transaural reproduction with two horizontal
front loudspeakers is unable to recreate virtual source in back and high or low elevations in the medianplane. Target virtual sources in all elevations in the median plane are perceived in front -horizontal
directions. In contrast, dynamic transaural reproduction with two horizontal front loudspeakers is able
to recreate virtual source in back or various high elevations in the median plane, at least for 3 kHz
low-pass filtered stimuli.
Actually, both spectral cue and dynamic cue contribute to front-back and vertical localization. The
spectral cue introduced by pinna is effective at high frequency above 5 kHz. It is also individual
dependent. A careful designed transaural reproduction may theoretically be possible to create thehigh-frequency spectral cue at the ideal listening position. Howeverˈdue to the short wavelength athigh frequency, the spectral cue is very sensitive to small deviation from the listening position andother error in the reproduction chain. In other words, transaural reproduction is unable to create stablehigh-frequency spectral cue. If timbre equalization is supplemented, the spectral cue is further
distorted. Therefore, front-back and vertical localization in transaural reproduction depend on
dynamic cue.
Wallach hypothesized that the ITD variation caused by head rotation allows the discrimination of
the front-back location as well as vertical displacement from the horizontal plane (9). Wallach’s
hypothesis has been validated by some modern experiment (5,9). As shown in Sec.3, in the case ofstatic reproduction, the information provided by ITD variation caused by head rotation is always
consistent with this of a source near the horizontal frontal direction. In the case of dynamic
reproduction, the information provided by ITD variation caused by head rotation matches with that oftarget or actual source. Of course, the incorrect spectral cue may cause another splitting
high-frequency virtual source in the horizontal-frontal direction. In addition, some front-backconfusion occurs at the target directions Φ S = 60º and 120º may be due to small ΔITD magnitudes atthese directions. And the large up-down confusion for low-elevation target directions of Φ S = -30º and210 º may be due to that the HRTFs of KEMAR without torso is used in present work. The torso-related
spectral cue at low frequency contribution to up-down discrimination, although head tilting also
provides supplementary information for up-down discrimination (9).

7. CONCLUSIONS
Transaural reproduction is unable to provide stable high-frequency spectral cue, therefore

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front-back and vertical localization depend on dynamic cue. Dynamic transaural reproduction with
two horizontal-frontal loudspeakers is able to provide correct dynamic cue and therefore is able tocreate virtual source at back and various elevations, at least below 3 kHz. Static reproduction is unable
to do so, and the perceived virtual source is usually limited in the frontal-horizontal plane.
Recently, mulichannel sound with height is developed rapidly. It is sometimes desired to downmix
multichannel sound signals for reproducing with fewer loudspeakers. Transaural processing has beensuggested for downmixing. The limitation discussed in present work should be considered when the
downmixing scheme is designed.

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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