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

Predicting Externalization of Anechoic Sounds
Robert BAUMGARTNER; Piotr MAJDAKAcoustics Research Institute, Austrian Academy of Sciences, Austria

ABSTRACTThe perceptual association of a sound with a source surrounding the listener is natural but requires complex
signal processing to be achieved in virtual or augmented realities presented via headphones. Little is known
about the set of spatial features required to elicit an externalized auditory percept, even under anechoic
conditions. We investigated the diversity and relevance of different features by conducting a model-based
meta-analysis of psychoacoustic studies. As potential features we considered monaural and interaural
spectral shapes, spectral and temporal fluctuations of interaural intensity differences, interaural coherence,and broadband inconsistencies (trading) between interaural time and intensity differences in a framework oftemplate-based auditory models. Our model predictions indicate that the monaural spectral shapes and thestrength of time-intensity trading present potent cues to explain most previous results.
Keywords: Head-related transfer functions, Virtual auditory reality, Computational modeling

1. INTRODUCTION
Virtual reality systems aim to immerse a listener into a well-externalized three-dimensional auditory
space. This requires a perceptually accurate simulation of the listener’s natural acoustic exposure.
Particularly challenging is to appropriately represent high-frequency spectral cues induced by the
pinnae because their morphology is very specific to the listener. To simplify this task, we aimed atdeveloping a phenomenological computational model for sound externalization with a particularfocus on spectral cues. The model was designed to predict a listener’s degree of externalization
based on binaural input signals and the listener’s individual head-related transfer functions (HRTFs)
under static, anechoic listening conditions.
Previous psychoacoustic experiments assessed sound externalization by subjective distancecomparisons (1–7) and/or the discriminability between real and virtual sound sources (5,8). Thesestudies showed that the externalization of anechoic sounds is not affected by broadband
approximations of interaural phase differences (5) but may slightly degrade if interaural time delays(ITDs) and interaural level differences (ILDs) are inconsistent (7). The auditory cortex contains an
integrated code of sound laterality, but also retains independent information about ITD and ILD cues.
This cue-related information might be used to assess how consistent the cues are, and thus, howlikely they would have arisen from the same source (9).
While reverberation is essential to accurately estimate the distance of a sound source(10),reverberation alone is not sufficient to externalize a sound (2,6). In order to be externalized, sounds
need to provide spectral cues in the direct path (1,6). Spectral cues are most effective in the highfrequency range of pinna cues (2) but saliency of spectral cues is also important if sounds do notcontain energy at those high frequencies (2,6).
Past studies on spectral cues of spatial hearing mainly focused on sound localization insagittal planes. Several localization studies suggest that the auditory system processes spectral cues
within monaural pathways (reviewed in 11). Animal studies (12) and model simulations (11) provide
further evidence that this process might focus on analyzing positive gradients in the stimulus
spectrum, but clear human psychoacoustic evidence is still missing and the transferability offindings from directional localization to sound externalization needs to be clarified.
A recent attempt to model the effect of spectral cue saliency on sound externalizationcompared interaural spectral level differences between the stimulus and internal reference templates(6). However, interaural spectral comparisons are in contradiction to the current understanding of
the monaural processing of spectral localization cues and to previous experimental results showingthat spectral manipulations degrade externalization also if interaural differences are preserved (5).

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By conducting a model-based meta-analysis, this study aims to clarify the auditory
mechanisms of spectral cue processing for auditory externalization and, in particular, the perceptual
weighting of spectral cues in comparison to other spatial auditory cues.

2. METHODS
2.1 Model
The model architecture generally follows a template-matching procedure applied to a set of different
cues (Figure 1). The model evaluates positive gradients in the spectral shape of magnitude profiles(MSG; c.f., 13), the spectral shape of ILDs (ISS; c.f., 6), the spectral standard deviation of ILDs
(ISSD; c.f., 14), the inconsistency between ITD and ILD (ITIT), and the interaural coherence (IC) as
summarized in Table 1. As a control cue, we also evaluated the difference in overall sound pressurelevel between target and template stimuli considering that loudness differences between theconsecutively presented stimuli may have affected the perceptual ratings.
Cue
MSG
ISS
ISSD
IC
ITIT
SPL

Table 1 – Externalization cues evaluated within the model
Description
Monaural spectral gradients (c.f., 11,13)Interaural spectral shape (c.f., 6)
Interaural spectral standard deviation (c.f., 14)Interaural coherence (c.f., 15)Interaural time-intensity trading (ITD vs. ILD)
Overall level difference between target and reference stimulus

Targ e t
e xcita tion pa tte rns

Gra die nt
e xtra ction

Te mplate
e xcita tion pa tte rns

Gra die nt
e xtra ction

Mona ura lcompa ris on
Bina ura lwe ighting

Ma pping toe xte rna liza tion

S am e for right e ar
Targ e t
e xcita tion pa tte rns
Te mplate
e xcita tion pa tte rns

LR

Inte ra ura lcue (s )Inte ra ura lcue (s )We ighte dcompa ris on

Ma pping toe xte rna liza tion

Figure 1 – Investigated structures of externalization models based on monaural (top) and/or interaural(bottom) cue template comparisons
ITDs were derived from binaural signals low-pass filtered at 3 kHz by extracting the time lag thatyields maximum IC of the temporal energy envelope (“MaxIACCe lp” in 16). Overall level
differences denoted the difference in dB RMS levels between the target and reference stimuli,
thresholded by a just-noticeable difference (JND) of 1 dB and averaged across ears.
All other cues were evaluated after filtering the target and template signals through a bank offourth-order Gammatone filters with a regular spacing of one equivalent rectangular bandwidth. We
computed the logarithm of the root-mean-square (RMS) energy within every frequency band toobtain spectral excitation profiles (c.f., 13). Audibility thresholds for band-limited signals wereapproximated by generally considering stimulus sound pressure levels of 70 dB and a within-band
threshold of 20 dB. To allow the evaluation of temporal fluctuations, the profiles were evaluated in
non-overlapping blocks of 5 ms, which has been considered as the integration time for spectral cues
(17,18). Assuming stationary input signals, the spectral profiles were averaged over time.

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The IC metric was denoted as the IC difference between target and reference:𝑑"# = 𝐼𝐶' − 𝐼𝐶) with 𝐼𝐶 = 𝑙𝑖𝑚 𝑖𝑛𝑓/∫ 12 (45/)17 (4)849∫ 12 (4):17 (4):84

and 𝜏 ∈ [−1,1] ms.

(1)

For the ISSD metric, the model evaluated standard deviations of ILDs across frequency bands,
computed the absolute difference of these deviations between the target and template, relative to thetemplate deviation:
ABC D"EBF (G)H

(2)

𝑑"AAB = 1 − AB D"EB (G)H.
C

7For the ISS metric, absolute differences between the target and template ILDs were evaluated,then differences smaller than 1 dB, considering JNDs of ILDs to exceed this range (Mills, 1960),
were set to zero and remaining differences were normalized by the template ILDs and finallyaveraged across frequency bands:I"EB (G)5"EB7 (G)(3)
𝑑 = ∑ L F
L.
"AA

JC

G

"EB7 (G)The ITIT was denoted as the difference magnitude between target-to-template ratios of ITD
and ILD (averaged across frequency bands):
M"'BF
M"EBF
(4)
𝑑
=L
−
L,
"'"'

"'B7

"EB7

with 𝛥𝐼𝑇𝐷' = 𝐼𝑇𝐷' − 𝐼𝑇𝐷) of 0 if smaller than 20 µs, 𝛥𝐼𝐿𝐷' = 𝐼𝐿𝐷' − 𝐼𝐿𝐷) of 0 if smaller than
1 dB.
For the MSG, positive spectral gradient profiles were obtained by differentiating theexcitation profiles (𝑝(𝑓) → 𝑝’(𝑓)) and softly restricting the value range by an elevated arctangent as
proposed in (13):^^(5)
𝑀𝑆𝐺 = 𝑎𝑟𝑐𝑡𝑎𝑛 \𝑝′(𝑓) − ` + .
__These gradient profiles were then compared between the target and template separately for each ear
by applying the same procedure as for the ISS metric, that is, calculating absolute target-to-template
differences, normalizing differences larger than 1 dB by the template gradients, and finallyaveraging those differences across frequencies. The MSG distance metrics for the two ears werethen combined according to the binaural weighting function defined in (11), effectively increasing
the perceptual weight of the ipsilateral ear with increasing lateral eccentricity:
8
58
(6)
𝑑
= def,g def,h + 1,
bAc

Iij kl⁄mwith 𝜙 ∈ [−90°, 90°] denoting the lateral angle (left is positive) and 𝛷 = 13°.
Similarly for all metrics, an exponentially decaying mapping function with the exponent
reciprocally scaled by the sensitivity parameter 𝑆uvj was used to map cue-specific deviations 𝑑uvj
from the template to externalization scores 𝐸uvj .
2.2 Assessment
Prediction errors are defined as the RMS of differences between actual and predicted externalization
score ratings normalized by the range of the rating scale used in the individual study. Optimal cuespecific sensitivity parameters are obtained by minimizing the prediction error individually for eachstudy. The model’s performance is assessed for various conditions collected from a representative
set of experiments (1,2,5,6).

3. Results
3.1 Effects of low-frequency alterations
Hartmann and Wittenberg (5) synthesized the vowel /a/ with a tone complex consisting of 38
harmonics of the fundamental frequency of 125 Hz, yielding a sound bandlimited up to 4750 Hz.
This sound was presented via headphones and filtered with individualized HRTFs. In one
experiment, the magnitudes of all harmonics up to a certain harmonic n’ were set to the interaural2171

average, effectively removing ILDs up to that harmonic’s frequency. In the other experiment, theipsilateral magnitude spectrum was flattened up to n’ while the contralateral magnitudes were
shifted in parallel, effectively maintaining the original ILDs but changing the monaural spectral
profiles. In both experiments, the listeners were asked to rate the degree of auditory externalization
on a continuous metric scale with minimum values referring to inside-the-head localization andmaximum values referring to localization at the actual loudspeaker position.

Figure 2 – Model simulations to predict the effect of low-frequency alterations up to a certain harmonic of acomplex tone with a fundamental frequency of 125 Hz. Actual data from Figures 7 and 8 from (5)The results in Figure 2 (left) show that externalization degradation induced by ILDs successively
set to zero were well predicted by the ISS, ITIT, and SPL cues. The more harmonics at which ILDs
have been removed, the more the target ISS is flattened and deviates from the template ISS, thesmaller is the average ILD in comparison to the constant ITD, and the higher is the SPL. The ISSD
cue leads to non-monotonic predictions that strongly depend on the center frequencies of peaks inthe spectral shape of the template ILDs. IC differences are very small and thus noisy. The MSG cue
is rather insensitive to the changes in ILDs because at low frequencies the complex acoustic filteringof the pinnae is negligible and thus monaural spectral shapes are quite similar at both ears and only
marginally affected by interaural averaging.
The degradation induced by flattening the ipsilateral spectrum while maintaining the original
ILDs (Figure 2, right) was well predicted by the MSG cue only. Predictions based on interaural cues
perform poorly because the experimental condition is designed to not affect these cues.
Overall, the MSG cue yields the smallest prediction errors across both experiments, whereby there isa marked difference in predictive power between the two different experimental manipulations. Theinteraction term comprising MSG and ITIT performs best overall.
3.2 Effects of spectral smoothing
Hassager et al. (6) presented Gaussian white noise bandlimited from 50 to 6000 Hz. These sounds
were filtered with individualized BRIRs (RT60 between 300 and 600 ms) in order to simulate soundsources positioned at azimuths of 0° and 50°. As independent experimental variable, Gammatone
filters with various equivalent rectangular bandwidths (ERBs) were used to spectrally smooth thedirect path portion (until 3.8 ms) of the BRIRs. Filters with larger ERBs more strongly smoothed theshape of the magnitude spectrum. Similar to the previous study (5), listeners rated auditory
externalization on a continuous scale.
Model simulations were based on (anechoic) HRTFs because the original BRIRs were notaccessible. This is not critical assuming that only the direct path is relevant if also only the direct
path has been modified during the experiment. Despite the non-monotonicities of the ISSD cue andthe minor changes in IC and SPL, most predictions follow the systematic trend of externalization
degradation with increasing bandwidth factor (see Figure 3). Moreover, all these cues are consistent
with the actual results in that they are insensitive to spectral smoothing below one ERB. Overall, theactual results are best predicted on the basis of the MSG cue.

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Figure 3 – Model simulations to predict the effect of spectral smoothing on the externalization ofsounds from various azimuths (0° and 50°). Actual data represent direct-sound condition from (6)Baumgartner et al. (1) also tested 15 normal-hearing listeners on the effect of spectral
smoothing but focusing on the high-frequency range between 1 to 16 kHz where the pinna induces
the most significant directional spectral variations. In contrast to the other studies, listeners judged
auditory externalization not absolutely but relatively within paired comparisons. Absolute
externalization scores were then estimated from the paired judgements via probabilistic model
fitting (19). Only scale estimates yielding fitting statistics within a heuristic range of 0.001 < 𝜒 _ <10were considered trustworthy and used for evaluation. Scale estimates for six out of twelve
listeners fulfilled this requirement.
Model predictions were based on listener-specific HRTFs and also assessed against listenerspecific results. As a consequence of large inter-individual differences the errors are comparably
high, while the average predictions shown in Figure 4 are still similar to the actual results. The IC
and SPL cues yield particularly poor results, whereas all other cues perform quite similarly acrossthe limited set of experimental conditions.

Figure 4 – Model simulations to predict the effect of spectral smoothing on the externalizationof sounds from various azimuths (±90° or 0°). Actual externalization scores estimated from pairedcomparison data from (1)2173

3.3 Effects of binaural microphone casing and stimulus bandwidth
Boyd et al. (2) presented broadband speech samples and used individualized BRIRs to simulate atalker positioned at 30° azimuth. They compared externalization ratings for in-the-ear (ITE) andbehind-the-ear (BTE) microphone casings as well as broadband (BB) and 6.5-kHz-low-pass (LP)filtered stimuli at various mixing ratios with stereophonic recordings providing only an ITD. The
amount of reverberation remained constant across mixing ratios.
For model simulations, original BRIRs were only available for 3 out of 7 (normal-hearing)
listeners. As suggested by earlier modeling work (6), spectral-shape cues (MSG and ISS) were only
evaluated for the direct path component of the BRIRs. Hence, for MSG and ISS, only the first 5 msof the BRIRs were used, faded-out by a cosine taper of 1 ms ending at the 5 ms. The simulation
results in Figure 5 show that all but the SPL and ITIT cues performed quite well.

Figure 5 – Model simulations to predict the effects of microphone casing and stimulus bandwidth
for various mixes between simulations based on individualized acoustics (100%) and ITDs only(0%). Actual data from (2) represents normal-hearing condition with one talker at 30° azimuth andreverberation. ITE: in-the-ear casing; BTE: behind-the-ear casing; BB: broadband stimulus;
LP: low-pass filtered at 6.5 kHz

4. DISCUSSION
Model simulations were conducted for three studies using (anechoic) HRTFs and one study using(reverberant) BRIRs. In all anechoic conditions, predictions based on either MSGs orinconsistencies between ITD and ILD (ITITs) performed very well. With results for high-passfiltered stimuli excluded, the overall picture for anechoic conditions seems to suggest that listeners
base their externalization ratings on the one of the two cues that indicates largest deviations fromthe reference sound. Under reverberant conditions, all interaural cues (ISS, ISSD, IC, ITIT) yielded
similarly small prediction errors, slightly favoring also the ITIT cue.
The sensitivity parameters used to scale the mapping function from cues to externalization
scores were optimized separately for every cue and study. Separate optimization is reasoned by thelimited quantitative comparability of subjective externalization ratings due to differently trained
subjects, different contexts, different experimental procedures especially with respect to presenting
reference stimuli, and many other methodological differences. Nevertheless, the optimization
procedure yielded similar sensitivity parameters for the favorite cues (MSG and ITIT) across studies,
which underlines the generalizability of our results.

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In all simulations template comparisons were only performed for the target direction, ignoringthat there could be a strong match to a template from another direction yielding strong
externalization. We did that because of two reasons. First, except for one study (1), listeners in all
the other experimental paradigms were asked to rate externalization against a fixed reference
stimulus. Hence, we assumed these ratings to be biased by the fixed reference location even though
it is hard to estimate how much these ratings were affected by directional localization changes, forinstance, within sagittal planes because of spectral cue changes. Second, listener-specific BRIRs forsource directions all around the listeners were not available.

5. CONCLUSIONSThe present investigations suggest that monaural spectral-shape cues are important for soundexternalization especially under anechoic listening conditions. However, the actual nature andprocessing of these cues is still poorly understood. The MSG cue implemented here has only been
motivated by physiological findings in cats and psychoacoustic model simulations in the context ofsagittal-plane sound localization. Future experiments could be targeted to clearly dissociated therelevance of positive vs. negative spectral gradients. Moreover, investigating this dissociation in
combination with a systematic variation of the amount of reverberation would allow to evaluate thetransition in perceptual relevance from MSG and ITIT under anechoic conditions to a potentiallybroader set of cues under reverberant conditions.

ACKNOWLEDGMENTS
We thank Bill Withmer for kindly providing the original data from Boyd et al. (2). This work was
supported by the Austrian Science Fund (FWF J 3803-N30) and Facebook Reality Labs.

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