Modeling binaural detection of a Gaussian noise target in the presence of alead/lag masker
Jonas BRAASCH(1) , M. Torben PASTORE(2) , Yi ZHOU(3)(1) Rensselaer Polytechnic Institute, USA, braasj@rpi.edu(2) Arizona State University, USA, torben.pastore@asu.edu(3) Arizona State University, USA, yizhou@asu.edu

Abstract
Recently, we presented the results of a binaural masked detection experiment in which a noise target was temporally embedded within a lead/lag noise masker pair [4]. The results show that the inter-stimulus interval (ISI)
between the masker and its reﬂection changed the detection threshold signiﬁcantly. For low ISIs of 2-ms, theaverage masked detection was −11 dB, but for a greater ISI of 20 ms, the threshold was much higher (−2 dB).
In the experiment, masked detection thresholds did not depend on whether the masker lead was on the same side
as the target (with the lag on the contralateral side) or the other way round.
Keywords: Binaural Hearing, Binaural Masking Level Difference (BMLD), Precedence Effect1

INTRODUCTION

In reverberant environments, sound source localization is often dominated by the directional cues of the wavefronts that propagate directly from the sound source and precede the arrival of reﬂections off nearby surfaces.
That is, despite the presence of reﬂections that arrive along many different trajectories, listeners’ perceived location of sound sources often corresponds closely with the actual location of the sound source itself. This iscalled the precedence effect (PE). Two competing theories exist to explain the precedence effect. One assumes
that the auditory system at least partly “removes” the lag stimulus from the incoming signal and then estimates
the position of the sound source based on the remaining signal (Research Hypothesis I – signal removal). This
could occur as the result of neural processes not speciﬁc to the PE (e.g., [8]) or mechanisms speciﬁcally purposed for the PE (e.g., [2]). Another theory assumes that the auditory system “disregards” the localization cuesof the lag signal and estimates the location of the sound source based on the directional cues of the lead (Research Hypothesis II – cue disregard) [9]. The present study reported here used a masked detection experimental
paradigm to investigate which of the two research hypotheses is correct. For this purpose, the detectability ofa target signal embedded in a lead/lag-based masker was tested. If the lagging stimulus is removed (Research
Hypothesis I), the test participants would have clear access to the lead signal on its own and the results would
then be similar to those where the same target is embedded in a masker with no lag. If, instead, the lag stimulus remained during auditory processing but the directional information of the lag was minimized (Research
Hypothesis II), the results for both test conditions should differ substantially because the lag would continue toact as an additional masker.

2

PREVIOUS PSYCHOACOUSTICS STUDY

In this section, the results of a binaural detection threshold experiment from [4] are described that will beanalyzed in the next section. Masked detection thresholds were obtained using an adaptive staircase method
after Levitt [?] based on a three-alternative, forced-choice paradigm. In this experiment, Gaussian noise signals
were used for both the target and the masker. All signals were bandpass ﬁltered to restrict the frequency rangeof the signal to 200–1000 Hz using 128-coefﬁcients FIR ﬁlters. The masker duration was 500 ms with 20-ms
cos2 on and off ramps. The target duration was 200 ms with 5-ms cos2 on- and offset ramps. In all cases, the5779

S+M+ Condition

S+MA+ MB− Condition
TARGET
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MASKER 1

MASKER 1

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S+M− Condition

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MASKER 2

S+M+RM− Condition
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S+M−RM+ Condition
TARGETTARGET
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MASKER 1

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TARGET
MASKER 1
MASKER 1
TIME

Figure 1. Schematic for the six stimulus conﬁgurations.
target was always presented 200 ms after the masker onset. A masker-independent noise sample was used tocompute the target. The target signals were lateralized using an interaural time difference (ITD) of 300 μs. Six
different spatial conditions were tested for the masker – see also Figure 1:
1. Ipsilateral Masker Condition (S+ M+ ): The masker was spatially placed at the side ipsilateral to the target
using an ITD of +300 μs (dichotic masker).
2. Contralateral Masker Condition (S+ M− ): the masker was spatially placed at the opposite side using an
ITD of −300 μs.
3. Summing Localization Masker Condition, diotic masker: (S+ M+ M− ): using a masker with two identicalcomponents with simultaneous onsets. The ﬁrst component was spatially placed at the ipsilateral target
side using an ITD of +300 μs ms, the second presented contralaterally with an ITD of −300 μs.
4. Summed Uncorrelated (dichotic) Masker Condition (S+ MA+ MB− ): a masker pair as in Condition 3, butusing two summed uncorrelated pairs.
5. Ipsilateral Masker with Contralateral Reﬂection Condition (S+ M+ Rm− ): the masker was spatially placedat the opposite side using an ITD of −300 μs (dichotic masker) with an additional reﬂection from thesame side −300 μs, presented after an ISI of 2, 5, 10, or 20 ms.
6. Contralateral Masker w/ Ipsilateral Reﬂection Condition (S+ M− Rm+ ): the masker was spatially placed at
the opposite side using an ITD of −300 μs with an additional reﬂection from the opposite side +300 μs,

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0

S+MA+MB−

−2
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+

Threshold [dB]

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+

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Figure 2. Results of the detection experiment showing the detection threshold for a Gaussian noise-burst target
in the presence of a lead-lag pair masker as a function of the interstimulus-interval (ISI). The solid black curveshows the results for the contralateral masker lead. The dashed curve depicts the results for the ipsilateralmasker lead. The gray curves show the baseline conditions. Each data point shows the average over all ﬁve
listeners, the error bars depict the standard deviation – from [4].
presented after an ISI of 2, 5, 10, or 20 ms.
Figure 2 shows the results for all six conditions of the experiment. For the S+ M+ condition, the target andthe masker have the same spatial properties, the masked detection threshold was measured at −3 dB (graydashed line). For the S+ M− condition, where the masker was presented from the side opposite to the target,
the masked threshold was found to be −18 dB (gray solid line), indicating a spatial release from masking of 15
dB. Similarly, for the S+ M+ M− diotic masker condition, the masked detection was measured at −14 dB (graydashed-dotted line). In this case, the spatial release from masking was 11 dB. The highest masking threshold at−1.8 dB was found for the uncorrelated masker (S+ MA+ MB− ).
For conditions where the masker was a lead/lag pair (S+ M+ Rm+ and S+ M+ Rm− ), performance was nearly thesame regardless of whether the lead masker ITD favored the same or opposite side to the target. For bothconditions, the masking thresholds approach the threshold for the diotic masking condition at low ISI values
and approach the threshold of the uncorrelated masking condition at high ISI values. Also, variability is very
consistent across all the different conditions, with values between 1 and 2 dB.
When the target and masker were presented from the same direction (300 μs ITD), our baseline condition, thethreshold was −3 dB. This value is in general agreement with data by [1], who measured a −5 dB thresholdfor a 200-ms broadband noise target masked by conditions, 500-ms Gaussian noise masker (500-ms duration
with its onset preceding the target onset by 200 ms). The 2-dB difference between both studies can be easily
explained; the study reported here used band-pass ﬁltered signals instead of the broadband signals used byBraasch [1], so less information was available to the test participants for making a decision than in [1]. Goodet al. [7] previously showed that binaural masking level difference (BMLD), a measure of spatial release frommasking, strongly depends on the frequency range of sounds, in their case; low, mid, and high, using free-ﬁeld
signals, so the inclusion of more high-frequency energy in the stimuli of [1] could be expected to make a

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20ms ISI

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ILDs

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10 2ms ISI010LMLT [dB]LMLT [dB]

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right earLMLT [dB]LMLT [dB]left ear

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Frequency [Hz]100 250500 1000
Frequency [Hz]Figure 3. Monaural spectral changes resulting from interference between the leading and lagging masker components for different ISI values for an adjusted 0-dB target-to-masker ratio. The actual masker levels are shownfor different auditory bands as the difference to the target level. LM denotes the level of the masker, and LT
denotes the level of the target. A gammatone ﬁlterbank was used to simulate the auditory ﬁlters. Each bar
shows the mean result for 10 simulation runs using different noise samples. Error bars denote ±1 standard
deviation.
difference in results as well.
In addition, we found:
1. The effect clearly depends on the ISI, for long ISI we see the effect of the ipsilateral masker plus a sightthreshold elevation for an additional contralateral noise.
2. For short ISIs both ipsilateral and the contralateral masker components interfere and cannot be perceptually separated, leading to similar results as a diotic masker
3. Over the whole tested ISI range it does not make any signiﬁcant difference if the ipsi or the contralateralmasker component comes ﬁrst, meaning there is no evidence for the PE effect playing a role here.

3

BINAURAL CUE ANALYSIS

Binaural and monaural cues were analyzed within auditory bands to understand how the direct sound masker
and the reﬂection interfere at different ISIs. The leftmost column of Fig. 3 shows the computed level differences
between the masker and the target for the left ear, therewith, if both the masker and the target have the samelevel before the reﬂection is applied. The second column from the left depicts the computed level differences
between the masker and the target for the right ear. At an ISI of 2 ms, the reﬂection cancels out the signal at afrequency of 250 Hz, because 2 ms is half the period of a 250-Hz sine tone, shifting this frequency componentout of phase. Since both the direct (lead) masker signal and its reﬂection (lag) have ITD cues pointing in

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Figure 4. All possible pairwise comparisons with a Student’s t-test. Individual conditions are listed in theleftmost column. For conditions which included a lead/lag masker pair, the delay between lead and lag (inmilliseconds) is indicated within square brackets. All other columns show the comparisons, with the listed
number of the comparison condition indicated at the top of each column. For example, the p-value for thecomparison of the the 5-ms ISI S+ M+ R− condition with the same condition but with a 10-ms ISI is shown at
the intersection of the 6th row and the 7th column.
opposite directions, the actual delay of the reﬂection is 2.3 ms in the left ear and 1.7 ms in the right ear. This
explains why the minimum level difference is observed at two different frequency bands for the left and rightear signals. In both cases, the minimum level difference is slightly less than −10 dB. At this frequency, themasker signal is about 10 dB below the target signal if the nominal target-to-masker level difference is 0 dB.
At an ISI values of 5-ms, the cancellation frequency declines to 100 Hz. While this frequency is below thelower cut-off frequency of the stimuli, residual energy still exists because of the roll-off characteristics of thehigh-pass ﬁnite-impulse-response ﬁlter (Matlab function ﬁr1.m with 128 ﬁlter coefﬁcients). At the right ear,the lowest masker-to-target level difference is found in the 100-Hz band with a value of −6 dB. At the 10-ms
and 20-ms ISI values, the masker level no longer varies much from the average level difference of 3 dB in
the relevant frequency range. The 3-dB value corresponds to the level increase found for adding two equallyintense uncorrelated noise sources.
Further, it was expected that the threshold for the condition with the additional uncorrelated noise masker(S+ MA+ MB− ) of approximately −2 dB, would be even higher than the baseline condition. The additional
masker component only affected the masked detection threshold slightly, because its spatial properties differ
from the congruent spatial cues of the ﬁrst masker component and the target. The BMLD between the S+ M−
and S+ M+ conditions was 15 dB, which corresponds to the general BMLD for the M0 Sπ versus Mm Sm condition cited in the literature [11] (Table 12.2).
Listener performance for the conditions with lead-lag pair maskers (S+ M+ Rm− and S+ M− Rm+ ) was highly
dependent on the inter-stimulus interval (ISI) between the lead and the lag masker components. However, it
made hardly any difference whether the lead masker was presented from the same or opposite side to thetarget. In general, the thresholds rose monotonically with the ISI. When the delay between the ﬁrst and second
masker was 2 ms ISI, the results were similar to those of the diotic masker condition (S+ M+ M− ). In fact, thediotic masker condition can be seen as a special case of the lead/lag pair masker with an ISI of 0 ms wherelead and lag arrive simultaneously. The measured thresholds for stimuli with lead/lag masker pairs were similar
to those found by [6] who tested a lead/lag pair masker (noise or talker) for a ﬁxed ISI setting (4 ms). For
the noise masker the authors found no BMLD improvement, but for the talker interference, the BMLD was in
the order of 6 dB for most conditions. The authors mainly attribute the improvement to informational masking5783

effects. Similar to our ﬁndings, [6] found that which side lead and which side lagged also made essentially no
difference to the results for both noise and speech.
In this context, it is noteworthy that the echo threshold, and therefore the ISI dependency on the lag’s impact, ishighly signal dependent as previous studies have shown – e.g., see [5]. However, more important than the actual
values is the general trend that the perceptual inﬂuence of the lag on detecting the target highly depends on the
ISI. For low ISIs, the lead-lag pair demonstrates spatial properties that perceptually differ from the spatial cuesof the target, while for high ISIs, the lead-lag pair behaves like an uncorrelated noise pair. For high values of
ISI, one of the underlying signals has the same spatial properties as the target, causing a relatively high masked
detection threshold.
For the low ISI conditions, we assume that the signals interfere with each other and produce new spatial cuesthat can be used by the listener to spatially separate the target from the masker. Studies, such as [3] and[10] have shown that for small ISIs two interfering ITD-based signals that are identical except for a delay can
produce very high Interaural Level Differences (ILD) due to interference effects. In both cases (high and low
ISIs), the temporal order of the arrival of lead and lag does not matter.

4

CONCLUSIONSIn a sound localization tasks, the auditory system largely disregards the information from the later arriving signals if lead and lag are identical and the delay between both signals is within a few milliseconds. For detection
tasks, however, the temporal order does not matter and the hypothesis that that auditory system completely
removes the lag from the superposed signal (Research Hypothesis I) can be ruled out. These considerations,
together with the results presented here, suggest that the PE does not need to be taken into account to explain
our data. The interference between the direct sound and the reﬂection for small ISIs leads to energy reductionsin isolated frequency bands. The magnitude of these reductions is in the same order as the threshold decreasemeasured from the 20-ms ISI condition. For small ISI’s, the interference effects also create large shifts inbinaural cues in isolated auditory bands.

ACKNOWLEDGEMENTS
This material is based upon work supported by the National Science Foundation under Grant Nos. BCS-1539276
and NSF BCS-1539376, and the Cognitive and Immersive Systems Laboratory (CISL).

REFERENCES[1] J. Braasch. Auditory Localization and Detection in Multiple-Sound Source Scenarios. VDI Verlag, Duesseldorf, 2002.
[2] J. Braasch. A precedence effect model to simulate localization dominance using an adaptive, stimulus
parameter-based inhibition process. J. Acoust. Soc. Am., 134(1):420–435, 2013.
[3] J. Braasch, J. Blauert, and T. Djelani. The precedence effect for noise bursts of different bandwidths. I.
Psychoacoustical data. Acoust. Sci. & Tech., 24:233–241, 2003.
[4] J. Braasch and M. T. Pastore. Binaural detection of a gaussian noise target in the presence of a lead/lag
masker. J. Acoust. Soc. Am., 143(1):EL49–EL54, 2018.
[5] J. Braasch, H. V. Savitala, and J. Blauert. Modeling the precedence effect for percussive sounds with different attack transients. In 19th International Congress on Acoustic, pages PPA–05–001–IP, Madrid, Spain,
Sept. 2-7 2007.

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[6] R. L. Freyman, K. S. Helfer, D. D. McCall, and R. K. Clifton. The role of perceived spatial separation in
the unmasking of speech. The Journal of the Acoustical Society of America, 106(6):3578–3588, 1999.
[7] M. D. Good, R. H. Gilkey, and J. M. Ball. Binaural and Spatial Hearing in Real and Virtual Environment,compendium The Relation Between Detection in Noise and Localization in Noise in the Free Field, pages
1108–1117. Lawrence Erlbaum Associates, 1997.
[8] K. Hartung and C. Trahiotis. Peripheral auditory processing and investigations of the “precedence effect”
which utilize successive transient stimuli. J. Acoust. Soc. Am., 110:1505–1513, 2001.
[9] W. Lindemann. Extension of a binaural cross-correlation model by contralateral inhibition. I. Simulationof lateralization of stationary signals. J. Acoust. Soc. Am., 80:1608–1622, 1986.
[10] M. T. Pastore and J. Braasch.
138(4):2079–2089, 2015.

The precedence effect with increased lag level.

J. Acoust. Soc. Am.,[11] W. A. Yost. Fundamentals of Hearing: An Introduction. Academic Press, San Diego, 4th edition edition,
2000.

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