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

Perceptual relevance of speaker directivity modelling in virtualrooms
Henning STEFFENS1; Steven VAN DE PAR2; Stephan D. EWERT3
1

CvO University, Acoustics group, Oldenburg, Germany

2

CvO University, Acoustics group, Oldenburg, Germany

3

CvO University, Medical Physics, Oldenburg, Germany

ABSTRACTSound sources like a human speaker, musical instruments and loudspeakers typically radiate sound with afrequency-dependent directivity pattern. If a human speaker faces the receiver, more high-frequency
components reach the receiver as when the speaker turns in the opposite direction. This is perceptually easily
detectable, particularly in anechoic conditions. In rooms, early reflections and late diffuse reverberation,
which both can be differently affected by the directivity pattern of the source, occur in addition to the direct
sound. While source directivity appears relevant for distinct early reflections, it is unclear to which extent theperceptual effects average out for later reflections and diffuse reverberation.
Here we assess to what extent directivity of a human speaker should be modelled for early reflections anddiffuse reverberation. For this we used a hybrid approach to simulate and auralize binaural room impulse
responses [Wendt et al., JAES, 62, 11 (2014)], combining an image source model (ISM) for early reflections
with a feedback delay network for diffuse reverberation. The approach was extended by a directivity filter
based on a spherical head model. Listeners distinguished between source orientations solely based on
ISM-directivity and detected average source directivity filtering even in reverberant conditions.
Keywords: Source directivity, room acoustics simulation, psychoacoustics

1. INTRODUCTION
Directivity of a human speaker in a room can be easily demonstrated when the speaker turns in the
opposite direction of a listener. The directivity pattern of the head and mouth radiate high frequencies
more directed to the front while low frequencies are radiated omni -directionally. Depending on the
acoustic properties of the room, head rotation of the source causes changes in the spectral pattern ofthe early reflections in addition to changes in the direct sound, most notably in the high frequencies.
For later reflections and diffuse reverberation, the effect of source directivity can be assumed to be
more spatially averaged, due to the high number of spatially more even distribution of reflections in
the acoustic sound field of the room.
While interaural time differences (ITD), interaural level differences (ILD) and the
direct-to-reverberant ratio (DRR) influence the perception of a source’s location and distance,interaction effects between spectral and spatial cues for source directivity perception are still open
questions.
Perception of sound source orientations was investigated by Neuhoff and colleagues. In (1)listeners had to indicate the orientation of a loudspeaker in front of them in a semi-anechoic room withbroadband noise as test signal. Results showed that test subjects were sensitive to the facing angle of adirectional sound source with better performances at closer distance and the source directly facing thelisteners.
Nakano et al. (2) performed experiments with a human speaker in real and anechoic environments.
With an average horizontal orientation error of 24.5° in anechoic and 33.8° in realistic (unfurnished)conditions, they concluded that it is more difficult to perceive orientation of a speaker in a real
1henning.steffens@uni-oldenburg.desteven.van.de.par@uni-oldenburg.de
3
stephan.ewert@uni-oldenburg.de22651

environment than in an anechoic room. Their results match with Kato et al. (3) and they found no
significant training effects for central frontal positions.
Edlund et al. (4) found that judging different facing angles of a human speaker is also possible withthe presence of background noise in furnished, asymmetric rooms and tends to be easier under certain
geometrically conditions (i.e. reflections of a nearby window) than in anechoic rooms.
In the above studies, important perceptual cues for the orientation of the sound source are changes
in the coloration of the direct sound or ILDs introduced by the effect of directivity on soundreflections.
Modelling the acoustic properties of source directivity within computer-generated auralizations
had been identified as an important factor for a perceptually plausible experience. Otondo (5) showedthat the directivity of a musical instrument has a direct influence on the distribution of acousticalparameters in a room, which is perceptually perceivable. This is supported by studies from Vigeant andcolleagues (6). A recent study by Budnik et al. (7) showed significant improvements when comparing
artificial-head-based binaural recordings of human speech in a classroom scenario with room
simulations including realistic speaker directivity with an omni-directional source.
While source directivity appears relevant for distinct early reflections, it is unclear to which extent
the perceptual effects average out for later reflections and diffuse reverberation and could therefore be
simplified for source directivity in room acoustics simulations. The current study assessed thisquestion by conducting two listening experiments with a human speaker as sound source in two
simulated rooms. Source directivity was simulated with a simple directional filter approach.

2. METHODS
A hybrid approach proposed by Wendt et al. (8; room acoustics simulator, RAZR) to simulate andauralize binaural room impulse responses (BRIRs) was used in the current study. RAZR combines animage source model (ISM) by Allen and Berkley (9) for calculation of early reflections with afeedback delay network (FDN) by Jot and Chaigne (10) for diffuse reverberation. This method
achieves perceptually plausible simulations with relatively fast computation time. The auralization
uses headphones and considers the rotation of the listener’s head.
The framework was extended with the option to include rotation of a virtual source as well as asource directivity filter to account for the spectral directivity pattern of the source.
2.1 ISM Source Directivity
In a closed-form ISM for a shoebox-shaped room, the exit angles of each ISM source can be gainedby calculating the vector between source and receiver from their relative positions and orientation. As
all walls are orthogonal and can be chosen to be axis aligned, either the x, y or z dimension has to beconsidered for each reflection. This is done by mirroring the initial vector depending on the ISM order.
From this the source exit angles can be easily obtained - for further information see (11).
The directivity of a human speaker was modelled with a simplified rotationally-symmetric source
filter based on the spherical head model (SHM) by Duda et al. (12). Originally intended for thereceiver to approximate head related transfer functions, here it is used to approximate the directivity ofthe mouth of the speaker as a sound source located on a sphere representing the head.
For the technical implementation a head-shadowing filter found in (13) was used. Figure 1 shows
the frequency responses for different input angles. Note that the filter response is normalized to be flatat zero degree (frontal direction of the source). For the back side of the source an attenuation of about
20 dB is observed 10 kHz.

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Figure 1 – Frequency responses for different azimuth angles of the normalized SHM-based head-shadow
filter.
2.2 Average Source Directivity Filter
Given an increasing number of reflections from many directions overlay for later reflections andlate reverberation, it is interesting to consider the radiated power of the source averaged across all
directions, expressed as an average source directivity filter. For this, the power spectral densities(PSD) of the source directivity filter were calculated for azimuth angels between zero and 180° in 2.5°
steps over frequency.
ܵ௫௫ ሺ݂ሻ ൌ ȁ‫ܪ‬ሺ݂ሻ  ȁ;

(1)

These PSDs were weighted over a sphere that was subdivided into ring surfaces with a width of
2.5°.
గ

ଶగ

‫ ܣ‬ൌ න ݀‫ʹܣ‬Ǥͷ ൌ න න ሺ ߠሻ݀ߠ݀߮
଴

(2)

଴

݀‫ʹܣ‬Ǥͷ ൌ ‫ ;ݎ‬ሺ ߠሻ݀߮(3)ܵመ௫௫ ሺ݂ሻ ൌ ܵ௫௫ ሺ݂ሻ ‫ʹܣ݀ כ‬Ǥͷ

(4)

The weighted PSDs per ring surface were summed and divided by the whole sphere surface forcalculation of an average transfer function:෡ ሺ݂ሻ ൌ ටቀ෍ ܵመ௫௫ ሺ݂ሻ ቁ Ȁ‫ܣ‬
‫ܪ‬

(5)

Finally, the inverse Fourier transformation of the average transfer function was calculated. The
resulting frequency response of average source directivity filter is shown in Figure 2.

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Figure 2 – Frequency response of the average source directivity filter based on the SHM.
2.3 Virtual Rooms
Two virtual shoebox-shaped rooms were used for the experiments: A small room (“Room L”) witha shorter reverberation time and a large room (“Room A”) with properties summarized in Table 1. The
setup of the virtual rooms with source and receiver locations is shown in Figure 3.The distance ofsource and receiver equals the respective critical distances (DRR of 0 dB for an omni-directionalsource) in the rooms.
Table 1 – Virtual Rooms
Name

Size [x, y, z], m

Volume, m3

T60, sCrit. distance, mRoom L: "Lab.”

4.97, 4.12, 3

61.4

~ 0.3

~1

Room A: "Aula"12, 30, 10

3600

~ 4.7

~ 2.5

Figure 3– Setup of virtual rooms, left: Room L, right: Room A.

3. LISTENING TEST I – IDENTIFICATION
A listening test with simulated ISM source directivity was conducted to investigate if listeners wereable to distinguish between different virtual source orientations. The tasked was to identify the correct2654

orientation of the source among four possible orientations (“Front”, “Left”, “Back”, “Right”). If the
speaker was facing the listener, “Front” would have been the correct answer.
Stimuli were played successively over headphones and the listeners had to provide a response via
four GUI buttons to continue. Eight trials per randomized orientation and virtual room were presented
and no feedback was provided. Five training trials per orientation and room (different sentence, withfeedback) were given before the test phase. Ten normal hearing listeners participated in the test (5female, 5 male, age 24-38, mean age 28.5).
3.1 Stimuli
An example sentence from the German Oldenburg Sentence Test (OLSA) (14) -“Britta bekommt elf
nasse Steine”-, spoken by a male speaker was auralized in central position via a third-order ISM in theabove mentioned approach in two virtual rooms (Table 1) for each orientation. For the training phasea different sentence spoken by the same speaker was used.
3.2 Results
The graphs in Figure 4 show the distributions of all answers derived from the confusion matrices
below, with a value of 1 representing 100 percent correct answers for one condition.

Figure 4 – Identification listening test results, left: Room L, right: Room A.
There were more correct identifications for each orientation in Room L than in Room A. In both
virtual rooms the ‘Front’ condition was identified best whereas the identification rates of the‘Left’/’Right’ conditions differ highly between rooms. Incorrect answers are evenly distributed.
3.3 Discussion
The results indicate that listeners are able to distinguish between different source orientations in thetwo simulated rooms with the proposed source directivity filter approach. Identification of ‘Left/Right’orientations benefits from the small Room L with strong and shortly arriving (about 13 ms) earlyreflections, whereas in the large and more reverberant Room A, reflections are stronger attenuated(and need longer to reach the listener) because of the larger traveling distances.

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For further statistical analysis, a resampling-bootstrap method was applied (15, 16), where it isassumed that all samples stem from the same underlying distribution and the difference in me ans
reflects the sampling variation for that distribution.
The frequency of observed differences that were as large as, or larger than the actual difference inmeans derived from randomly sampling the combined distribution of the Room L and Room A
conditions was calculated (1000 iterations). Here identification rates for ‘Left’ & ‘Right’ showed to besignificantly different (p < 0.05) between rooms.

4. LISTENING TEST II – DETECTION
In a second listening test, the question was approached if the simulation of source directivity can be
simplified by using the average source directivity filter at higher ISM orders, where a number ofspatially distributed reflections overlap. The hypothesis was that the effect of individually simulated
directivity of each image source is not perceivable for higher ISM orders compared to applying the
averaged source directivity.
Listeners judged in an ABX experiment whether the third stimulus out of three (ABA, ABB) was
the same as the first or the second one (X = A or X =B). Listeners had to provide their response via two
GUI buttons to continue. Sixteen trials per virtual room over two runs were presented with feedback
and no training phase. Ten normal hearing listeners participated in the test (2 female, 8 male, age 25-38,
mean age 29.8).
4.1 Stimuli
The “Right”-stimulus from the identification test was chosen for this experiment as reference. The
general auralization parameters were the same as in the identification experiment. In the test stimulus,
instead of correctly filtering all ISM stages with the source directivity filter (2.1), the average source
directivity filter (2.2) was utilized, starting from the third ISM order. This effectively applied theaverage directivity to the later reflections and diffuse reverberation while maintaining the correct
directivity in the direct sound and the early reflections.
4.2 Results
Figure 5 shows the percentages of the correct answers (median and interquartile ranges) for
detecting the reference and test stimulus both virtual rooms. A percentage of 50% indicates chancelevel. The median results are slightly above 60% and below the binomial significance level indicatedby the horizontal dashed line.

Figure 5 – Detection listening test results. The dashed horizontal line indicates the binomial significancelevel.

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To further analyze the results, a method proposed by Boley and Lester (17, 18, 19) was used todetermine the sensitivity index d’ as well as the 95% confidence interval (CI) per listener. The numberof listeners that detected a difference in the ABX experiment was determined by d’ ± 95% CI > 0. Twolisteners (4 & 7) were able to detect a difference in both conditions. One listener (9) did not detect any
difference in both conditions. Results of the remaining listeners show no clear tendency towards one
particular condition.
Table 3 – Calculated d’ ± 95% confidence per listener
Listener No.

Room L

Room A1

0.880±1.614

1.270±1.053

22.360±1.547

1.780±6.252

30.000±8.840

2.230±0.381

41.190±0.775

1.490±0.758

52.880±0.324

1.490±1.577

60.600±1.715

0.920±0.808

72.720±0.258

1.830±0.561

8

1.460±0.878

1.490±1.577

90.520±6.439

0.000±1.053

101.510±6.254

1.270±1.053

Σ(d’±95% > 0)54

4.3 Discussion
Overall the results do not allow to state that the effect of individual directivity against averaged
source directivity for the third-order image sources and late reverberation is not perceivable. Fivelisteners (Room L) and four listeners (Room A) out of ten distinguished both conditions. However, aslight tendency that detection is more difficult in the larger room A was observed.
It should be noted that the here employed virtual setup and stimuli just reflect one specificcondition out of a multitude of potential naturally occurring room condition s and source and receiverlocations. For the current two conditions, about half of the listeners could not detect any difference
between the more exact and approximated average simulation of the effect of source directivity in thethird-order reflections and late reverberation.

5. SUMMARY
A hybrid approach to simulate and auralize BRIRs was extended with a simplified source
directivity filter. Two experiments were performed to investigate perceptual effects of source
directivity modelling.
Despite the very straightforward approach, experimental results show that a perception of source
directivity can be achieved by a simple spectral filter within the ISM. The best performance wasobserved in the smaller room with strong early reflections from nearby walls.
A spatially averaged source directivity filter applied to later reflections and diffuse reverberation
was still detected by half of the listeners. While perceptually detectable in an ABX comparison test,
future research has to show which cues were used for detection and how relevant directivity modellingfor higher-order reflections is regarding perception of source orientation and evaluation of, e.g.,speech intelligibility in simulated room conditions.

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