The precedence effect as onset dominance observed at multiple levels of processing ? a modeling study

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The precedence effect as onset dominance observed at multiple levels of processing ? a modeling study

M. Torben Pastore

To cite this version:

M. Torben Pastore. The precedence effect as onset dominance observed at multiple levels of processing ? a modeling study. Forum Acusticum, Dec 2020, Lyon, France. pp.1195-1202,

�10.48465/fa.2020.0689�. �hal-03235926�

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The precedence effect as onset dominance observed at multiple levels of processing – a modeling study

M. Torben Pastore

¹

1 Arizona State University, United States of America

ABSTRACT

When two correlated long-duration stimuli are presented over headphones with different interaural time differences (ITD) and a short onset delay (1—5 ms) between the two stimuli, listeners typically indicate lateralization that is dominated by the ITD of the stimulus that was presented first. This localization dominance, a perceptual outcome of the precedence effect, was measured by Pastore and Braasch for a number of related conditions all based on long-duration noise bursts.

Modeling of peripheral and brainstem processing revealed that the results could be explained, to a first approximation, by the extraction of ITDs from the rising slopes of envelope fluctuations in the neural output of the auditory nerve during the onset and ongoing stimulus portions. Based on these modeling outcomes, this presentation will argue that the precedence effect may be conceptualized as instances of observed onset dominance that are integrated across different time scales and levels of auditory processing to form an overall perceived auditory percept that is dominated by the first arriving stimulus.

10.48465/fa.2020.0689 e-Forum Acusticum, December 7-11, 2020

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THE PRECEDENCE EFFECT AS ONSET DOMINANCE OBSERVED AT MULTIPLE LEVELS OF PROCESSING – A MODELING STUDY

ABSTRACT

When two correlated long-duration stimuli are presented over headphones with different interaural time differences (ITD) and a short onset delay between the two stimuli (1–

5 ms), listeners typically indicate perceived lateralization that is dominated by the ITD of the stimulus that was presented first. This localization dominance, a perceptual outcome of the precedence effect, was measured by Pastore and Braasch for a number of related conditions all based on long-duration noise bursts. Modeling of peripheral and brainstem processing revealed that the results could be explained, to a first approximation, by the extraction of ITDs from the rising slopes of envelope fluctuations in the neural output of the auditory nerve during the onset and ongoing stimulus portions. Based on these modeling outcomes, this presentation will argue that the precedence effect may be conceptualized as instances of observed onset dominance that are integrated across different time scales and stages of auditory processing to form an overall perceived auditory percept that is dominated by the first arriving stimulus.

1. INTRODUCTION

In reverberant spaces, early reflections can complicate sound source localization. Multiple early reflections that are highly correlated with the direct sound arrive at listeners’ ears from many different directions just after the direct sound. For non-transient sounds, such as speech or music, the leading direct sound and its lagging reflections combine constructively and destructively with each other, further degrading any localization cues they might carry. Under such conditions, we might reasonably expect to hear multiple sounds at multiple locations, or perhaps an incoherent, spatially non-distinct “blur.” Instead, listeners routinely perceive a single sound source located at or near the location of the sound source. That is, by virtue of preceding its reflections, the direct, first-arriving wavefront dominates perceived localization of the auditory event - the measure of this is called localization dominance. The con- ditions giving rise to this behavior, called the precedence effect (PE), are often simplified for experimental investigations. Beginning with the seminal study of [1], the PE has most often been studied by presenting a single lead click stimulus, with some combination of interaural difference properties to model the wavefront propagating directly from the sound source to the listener. An identical or closely-related stimulus, called the lag, is then presented after some lead/lag delay with different interaural properties to model a single reflection arriving after the direct

sound as a result of the greater distance it traveled. Within some range of lead/lag delays, listeners generally report a single, fused auditory percept at a lateral position that cor- responds closely with the perceived lateral position of the lead when presented on its own. There are essentially two reasons to study the PE. First, the PE is an important fa- cotor in much of sound source localization in reverberant environments, especially the built environment. By exten- sion, an understanding of the PE is important to consider in the design and construction of indoor and outdoor spaces where acoustics are important to the use of those spaces.

A second reason for studying the PE is that it offers a window into the non-linear, time-varying processing of the auditory system with stimuli and behavioral outcomes that can be simplified to the point where they can be modeled at a tractable level.

There is a large, varied literature on many of the outcomes of the PE, and reviews of the PE include [2, pp. 85–

105], [3, pp. 222–237], [4], and [5]. Nevertheless, though the literature is rich, a simple theory of the PE has thus far eluded our grasp – we are left with a sprawling set of apparently loosely-related behavioral outcomes and a few models that attempt to explain one set of data or the other.

The modeling presented here is motivated by the idea that a behavioral outcome that is widely observed across many areas of auditory and sensory research, operationally de- fined as “onset dominance,” might also offer an organizing principle for modeling the auditory processing that results in the precedence effect. In the present case, a concep- tion of the processing that results in the PE is modeled as the “chain reaction” of “onset dominance” at multiple, closely-related stages of peripheral and brainstem auditory processing. This model therefore makes the case that at least some outcomes associated with the PE simply ”fall out of the processing” with no dedicated PE mechanism per se. The modeling shown here is restricted to explain- ing the dominance of the lead ITD in perceived lateral responses to lead/lag noise bursts over headphones. Nev- ertheless, the framework of onset dominance at multiple levels may apply to percepts that occur over longer time periods, such as the“buildup of the PE,” the “Franssen effect,” and other phenomena closely related to the PE that may involve higher processing such as cognitive analyses to the plausibility of one perceptual estimate versus another (perhaps, for example, in avoiding a front-back re- versal, see [6].

First, behavioral data are presented. Then modeling analyses are explained and motivated using the concept of onset dominance at multiple levels of processing. The

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modeling outcomes are then compared to the behavioral data, and finally, the limitations and future directions of this effort are briefly discussed..

2. BEHAVIORAL DATA 2.1 Methods

While most testing of the PE has focused on click stimuli or trains of clicks, most everyday sounds, such as speech, are composed of a succession of longer, often contiguous, sounds. The furthest difference from a “click” may be a long-duration noise. [7–9] tested the PE over headphones using long-duration lead/lag noise stimuli and increased the intensity of the lag stimulus to ‘stress’ the mechanisms that result in the PE. The authors thereby sought to gain in- sights into the PE by observing the conditions under which the PE did and did not fail. For this presentation, only a few conditions are examined, where the levels of lead and lag were the same (i.e. 0 dB lead/lag ratio). More extensive and detailed analyses are offered in [9].

Dizon and Colburn [10] offered striking evidence that the ongoing portion of long-duration noise stimuli could induce localization dominance even when the gating onsets and offsets were diotically removed, though the lateral extent of perceived localization was not measured. In the experiments presented here, standard lead/lag stimuli and the same basic stimulus with gating onsets diotically windowed out were presented so that the relative influence of onset and ongoing stimulus portions on listeners’ perceived lateral response could be evaluated and modeled.

Figure 1 illustrates the two basic stimulus configura- tions. The lead was always presented with an ITD of ± 300 µs; the lag was presented with an equal and oppo- site ITD. The delay between the lead and lag, called the lead/lag delay was set between 0 and 5 ms in steps of 1 ms. In pilot experiments with 200-ms duration stimuli we found that lead/lag delays longer than 5 ms often induced “split images,” therefore lead/lag delays >5 ms were not tested. All stimuli were normalized and presented in a sound-isolated booth over Sennheiser HD-600 headphones at 70 dB SPL as measured with a Head Acoustics HMS-II.1 artificial dummyhead. For half the trials, stimuli were presented with the lead ITD favoring the left and the lag ITD favoring the right. For the other half of presentations ITDs were reversed. Stimuli were presented in blocks by stimulus type. Within each block, all combinations of lead/lag delay and lag level were presented (though only the 0-dB lag level is discussed in this presentation). All stimuli were presented in randomized, counterbalanced order. Each block was completed in approximately 20 min- utes and no more than 2 blocks were tested for any subject in the same day.

Participants used a trackball mouse to vary the ILD of the pointer so that their perceived intracranial position of the pointer matched that of the test stimulus. The pointer had a 500-Hz center frequency, 200-Hz bandwidth, 20- ms-cos²on/off ramps, and duration of 200 ms. The ITD of the pointer was 0 ms and the ILD was randomized be-

Figure 1. Time domain illustrations of the two lead/lag stimuli: a 200-ms noise burst (referred to as the 20020 stimulus), and a diotically windowed noise burst of the same duration duration (referred to as the 20020D stimulus). The stimuli had a 500-Hz center frequency with an 800-Hz bandwidth with 20-ms cos²on- and off-ramps. The ITD, the delay between the lead (or lag) in one ear and the lead (or lag) in the contralateral ear, was

±300 µs. The lead/lag delay was the time between the onset of the lead at one ear and the onset of the lag at the other ear. For the diotically-windowed 200²⁰Dstimuli, a 400-ms duration stimulus was created. Then, the lead/lag stimulus was multiplied by a temporally-centered diotic window with 20-ms cos²on- and off- ramps – indicated in the figure by the light gray overlays. This operation yielded a stimulus with a duration of 200 ms, the same as the 20020condition, with diotic onsets but the same ongoing temporal fine-structure relations that would occur in the “ongoing” stimulus portion of the standard long duration lead/lag pairs presented with the 20020stimulus.

fore each trial. Listeners could play the test stimulus and pointer as many times as they required, with a minimum of three times each before their answer was accepted. Re- peated presentations of either target or pointer stimuli were always separated by at least one second. When the listener was satisfied that they had matched their perceived lateral positions of the pointer and test stimulus, they pressed the space bar to record their answer and play the next stimulus. Listeners were asked to point to the center of the hor- izontal, intracranial position from which each sound event originated.

To compare data across listeners, a ‘reference’ condition was included in which only the leading stimulus was presented with an ITD of 0 µs, +300 µs, or −300 µs, presented in randomized order 9 times per stimulus. Vi- sual inspection confirmed that listeners perceived all diotic stimuli very close to midline. For analysis and plotting, pointer ILDs were then normalized as in [7–9, 11]. Briefly, the acoustic pointer ILDs listeners used to match their per-

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ceived lateral position of presented stimuli were scaled by the pointer ILDs they reported in the reference condition.

For example, if a listener indicated their perceived intracranial position of the lead/lag test stimulus using 75% of the ILD they had used to match the position of the single reference stimulus when it was presented with the lag ITD, then their response would be scaled to −0.75. See [7] for details.

2.2 Results

Figure 2. Normalized listener performance for the 20020 vs.

200_20Dconditions for 11 listeners. 20020stimuli had 20-ms cos² on- and off-ramps whereas the 20020Dstimuli had diotic 20-ms cos² onsets and offsets and an overall stimulus duration of 200 ms.

Figure 2 shows the averaged, normalized pointer ILDs used by 11 listeners to match their perceived lateralization of the 20020 (black circles) and20020D (grey triangles) stimuli. The figure is read the same as the three previous results figures. Two main patterns in listener performance emerge. With a few exceptions, lateralization is more to the midline for the20020Dthan the20020stimuli, suggesting reduced localization dominance and a weaker PE. For the 200^20Dcondition at lead/lag delays greater than 3 ms, listeners demonstrated localization that was only somewhat dominated by the ITD of the lead stimulus. Nevertheless, for lead/lag delays of 1–3 ms, listeners demonstrate localization dominance for the20020Dstimulus that is lesser but still comparable to that for the200²⁰condition, despite the diotic windowing of the gating delays between lead and lag for the20020Dstimulus. That is, these results show that, given sufficiently short lead/lag delays, localization dominance can result from cues that are, presumably, in the ongoing stimulus portion despite gating onsets that might be expected to produce lateralization to midline if onset dominance at the level of the entire stimulus was the same across stimulus conditions. [12] have shown evidence that appears to suggest that listener results for trains of lead/lag clicks might not be explainable based solely on the same monaural peripheral interactions invoked to explain the PE

for single sets of lead/lag click stimuli.

Also, as the data above, those of Dizon and Colburn [10] and those of Freyman and others have shown, the ongoing portion of long duration stimuli also has an effect on behavioral outcomes. That is, onset dominance is often in- complete. Freyman and Zurek [12] have suggested that the mechanisms involved in the ongoing PE, at least for trains of lead/lag clicks, may not be explainable based only on the same monaural peripheral interactions that appear to explain the PE for single sets of lead/lag click stimuli.

3. MODELING ANALYSES

3.1 Conceptual motivation for the modeling analyses Onset dominance is found throughout neural and sensory processing in general and is important to auditory localization in specific (e.g., [13], [14] [15]. Perhaps, in part, because most testing of the PE has focused on click stimuli, interactions that occur at stimulus onset have often been emphasized to provide explanation for the precedence effect [16–18]. This presentation considers the hypothe- sis that onset dominance can be observed at several time scales in the PE, and correspondingly, several different levels of auditory processing. A simple model based on biologically-inspired peripheral and brainstem processes is then constructed based on this conceptual framework and modeling analyses are compared with the behavioral data presented in the last section.

At the shortest time scale (≈1–5 ms), monaural, peripheral interactions at the level of signal transduction, such as ringing of the basilar membrane, compression, and adaptation at the synapse between the auditory nerve and in- ner hair cells (AN-IHC – see Fig. 4) can emphasize the neural representation of the leading portion at the onset of the overall stimulus, over acoustic elements, such as reflections, that arrive a few milliseconds later. As [20] have argued, these monaural, peripheral interactions are likely to play an important role in the binaural analysis that results in the PE. Indeed, [21] and [18] have shown that behavioral outcomes for lead/lag click stimuli presented over headphones are predictable to a remarkable degree using this explanation.

Additionally, [22], [23] has shown that ITDs during the rising slopes of the envelope of neural output from the auditory nerve are encoded preferentially over other portions of the neural output. This may be thought of as another example of observed onset dominance, and, combined with the properties of auditory nerve output, is an essential com- ponent of this model.

Onset dominance is also evident at a longer time scale, as shown by, for example, the Franssen effect (e.g., [24], [25]), and this seems likely to be the product of relatively more central processing. Single lead/lag click pairs, such as those used in the majority of PE studies, can not be expected to show evidence of such longer time-scale onset dominance. For example, [26] developed a testing paradigm using trains of lead/lag click pairs to in- vestigate the relative roles of onset and ongoing cues in

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Transduction - filter ringing - adaptation - compression

Cue Extraction - ITDs from rising slopes - ILDs

- effects of peripheral transduction on binaural difference estimates

Formation of Decision Variable - cue weighting based on variability of:

- ITD/ILD estimates

over time/with each other/across frequency - the resulting laterality estimates from onset vs. ongoing stimulus portions - listener strategy

A

B

"onset"

+

OD_global Lag

Lead

+ +

OD_local

{ {

"ongoing"

}

OD_local

OD_global

Figure 3. [A] Flowchart showing the three stages of processing considered in the modeling with their associated mechanisms.

Onset dominance can be observed in each of the three stages and all contribute to the degree of onset dominance at the overall stimulus level. [B] Conceptual illustration of the putative manifesta- tions of onset dominance considered in this report. Two wave- forms arrive at the two ears with some interaural delay. Within any given auditory band, fine-structure ITDs are extracted during the rising, onset portion of local envelope fluctuations while ITDs from subsequent portions of each envelope fluctuation are largely unencoded. This local onset dominance (ODlocal) is illustrated with solid gray lines, and is likely to occur in midbrain structures (i.e., lateral superior olive and inferior colliculus). The remaining two forms of onset dominance involve the weighting of local ITD estimates extracted from different stimulus portions to form an ITD estimate for the overall stimulus. This weighting is likely to occur at central levels of processing. The perceptual dominance of the local ITD estimate at the onset of the entire stimulus over other subsequent local ITD estimates, global onset dominance(ODglobal), is illustrated using a dashed line with an arrow covering the entire stimulus. For long-duration stimuli, envelope fluctuations within narrow-band auditory filters give rise to a succession of local ITD estimates within the ongoing stimulus portion after the stimulus onset. These accumulated local estimates may be integrated for an ITD estimate from the ongoing stimulus portion (solid light gray lines and “plus” symbols) that may then be weighted against the local ITD estimate extracted at stimulus onset. Color online.

a precedence-like paradigm. Freyman noted that stimuli with ambiguous ongoing ITD cues tended to be localized based primarily on the first ‘onset’ pair of clicks. When the ongoing portion of the click train had ITDs that were more consistent, the influence of the onset pair appeared to be diminished. The degree to which click trains, with alternating lead/lag pairs can predict behavior for longer-

Figure 4.Modeled auditory nerve output ( [19] showing adaptation and filter ringing as a function of filter center frequency and stimulus level. The stimulus was a 50-ms duration sinusoid at the center frequency of the relevant filter. Blue arrows show the difference between peak response and that which occurs 20-ms after stimulus onset. Note that any response after 50 ms is ringing of the filter.

duration noise stimuli is not clear.

Stecker [27] investigated the relative influence of onset and ongoing portions of precedence stimuli made from click trains and found that the onset dominates perceived lateralization when the interval between the clicks was less than 5 ms. As the interval between the clicks was increased beyond 5 ms, the binaural cues carried by the clicks were weighted relatively uniformly over stimulus duration (also see [14]). This result appears to be in keeping with the time scale of peripheral interactions discussed above. When a pause was introduced into the middle of the stimulus, the first click in the resuming second half of the stimulus was weighted more than other temporally surrounding clicks. A possible interpretation of this result is that, for long-duration stimuli, large envelope fluctuations across several auditory filters that are spaced far enough apart in time (perhaps 4 - 8 ms) could function essentially as onsets which could resume the effects of peripheral interactions such as those proposed by Hartung [20].

3.2 Model structure

This analysis attempts to answer these questions using simple peripheral and midbrain mechanisms that all appear to contribute to OD at both local (e.g., individual amplitude fluctuations) and global (e.g., the overall stimulus) levels.

This conceptual framework is schematized in Fig. 3 and explained in further detail in the figure caption. We con- ceptualize OD not as a mechanism or “force” in itself, but rather as an observed outcome brought about by mechanisms at peripheral, midbrain, and central levels of processing – this section makes the case that OD can be observed at each of these levels, and that these mechanisms all contribute together to the degree of onset dominance observed at the level of the overall stimulus. In this pre-

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sentation, only ITDs are considered. See [9] for further details and breadth.

The auditory nerve model of [19] was used because it includes various linear and non-linear mechanisms of peripheral processing (e.g., filter ringing, compression, and neural adaptation) that allow the examination of peripheral, monaural interactions that [20] and others have shown to be important contributors to the PE. Timing differences in afferent activity were extracted from the time-varying mean rates of the modeled auditory nerve fibers (ANF) in response to the PE stimuli presented at 70 dB SPL.

Figures 5 and 6 show initial analyses of the basic mechanisms, focusing on a single auditory band centered at 750- Hz. This frequency was chosen based on [7], which found that binaural differences in this frequency region were reasonably predictive of the general behavioral trends identi- fied in the data. The model then extracts the peaks (above a threshold of 20 spikes/sec) of the cyclic firing rate func- tions of the left and right ANFs. For ITDs, we computed the peak location difference in time between left and right ANF responses on a cycle-by-cycle basis. In light of the finding that ITDs encoded in the rising slope of the stimulus envelope are more reliably correlated with behavior than ITDs in the decay slope [22, 23], we further parti- tioned ITDs associated with the rising slope of the response envelope.

Note that the ongoing portions of the20020and20020D

stimuli were nearly the same, only their garting onsets were different. So, the ITD cues carried by bnoth stimuli can be analyzed by looking at the modeling results for the 20020 stimulus, with the caveat that, while both the onset ITDRS and ongoing ITDRS are available for the 200²⁰ stimulus, only the ongoing ITDRS is available for the 200²⁰ stimulus. However, keep in mind that the first few ITD estimates of the ongoing ITDRS would likely function as the onset ITDRS for the20020Dstimulus.

There are two ITD estimates shown for each modeled auditory filter – (1) “onset ITDRS,” estimated from only the first rising envelope slope at the onset of the entire stimulus and (2) “ongoing ITDRS,” integrated across the accumulated ITDRS that occurred after stimulus onset during the ongoing stimulus portion. The weighted mean/standard deviation of each of these three ITD estimates was calculated across the ten modeled auditory bands using the q(f ) ITD weighting function from [28], which approximates the relative saliency of ITDs for low-frequency stimuli across frequency as reported by [29]. The combined ITD estimates are then compared directly with the listener data for the200²⁰and200^20Dstimulus conditions.

Figure 5 shows model outputs for a single filter for the 2-ms lead/lag delay condition. For this stimulus, behavioral results for both stimuli were relatively similar. Model results for this filter and behavioral outcomes are compared at the right end of the figure panel. For this stimulus, the onset ITDRS (red diamond) and the mean of the ongoing ITDRS estimates across time (black diamond) both correlate closely with the behavioral response shown with the20020condition (green square) and 20020Dcondition

Figure 5. Top figure: Modeled auditory nerve output for the auditory filter centered at 764-Hz. Bottom figure: Detailed ITD analyses for the 20020stimulus for the 2-ms lead/lag delay condition with lead and lag of the same level.

(green upside-down triangle). Given this, it is difficult to gain any sense of the relative contributions of the onset and ongoing ITD cues.

Figure 6 shows initial modeling results for the 5-ms lead/lag delay,200²⁰and200^20Dstimulus conditions. For this stimulus, behavioral results for both stimuli were quite distinct, with perceived lateralization apparently dominated by the lead ITD for the20020stimulus and perceived lateralization near the midline for the 200^20D stimulus.

Even these single-filter modeling results mirror the behavioral results closely – compare the behavioral result for the 20020 stimulus (green square) with the onset ITDRS estimate (red diamond). Then, compare the behavioral result for the200²⁰ stimulus (green upside-down triangle) with the ongoing ITDRSestimate (black diamond with er- ror bars). It is clear from both Figures 5 and 6 that the empty (white) circles and diamonds, which represent ITDs extracted from stimulus portions where the envelope of neural output was not rising, do not correlate with the behavioral data well at all. The ITD estimates are therefore disregarded in the final modeling Figure 7.

Figure 6. Top figure: Modeled auditory nerve output for the auditory filter centered at 764-Hz. Bottom figure: Detailed ITD analyses for the 200²⁰stimulus for the 5-ms lead/lag delay condition with lead and lag of the same level.

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Figure 7.Modeled ITDs for the 200²⁰(top row) and 200²⁰Dstimuli (bottom row) at 0-dB lag level. Shaded circles, connected by thin black lines, represent ITDRScalculated during the first rising slope of the onset of the entire stimulus. Filled black squares, show ITDRS

calculated from the rising slope of within-filter envelope fluctuations during the ongoing portion of the stimulus. Open, unconnected circles show ITDs estimated from all stimulus portions, regardless of slope. Panels to the left show model results for the individual filters most heavily weighted in the ITD weighting function (center panel – filled triangles indicate center frequencies for which model results are shown). The center frequency for each filter is shown at the top of each individual filter model panel. Modeled ITDs for these individual filters are then weighted by the ITD weighting function (see text for more details). The weighted mean and standard deviation across center frequencies of all ten individual filters are shown in the rightmost column along with the behavioral data (thick shaded line). Behavioral data are plotted so that an average normalized pointer ILD of ±1 = ±300µs (see methods, reference condition).

Figure 7 shows modeled ITDs for all tested lead/lag delays at 0-dB lag level for the20020(top row) and20020D

(bottom row) stimuli. In the figure panels to the left, three types of ITD estimates are shown for ten modeled auditory filters spaced one Equivalent Rectangular Bandwidth apart. The figure panel entitled “ITD Weighting” shows the q(f ) ITD weighting function from [28]. Filled triangles indicate those frequency bands that are weighted most heavily – model results for these filters are shown in the individual panels to the left. The right-most column shows the mean and standard deviation of all ten filters, weighted by the q(f ) function for each of the two forms of ITD estimate discussed below.

Looking at the data for individual filters, the onset ITDRS (shaded circles) estimates are fairly consistent across filters for the 200²⁰ condition (top row), whereas this same estimate fluctuates wildly across filters for the diotically-windowed20020Dcondition (bottom row) – this difference in variability becomes clear in the weighted mean data when comparing the errorbars for the onset ITDRS, showing the weighted standard deviation between filters, accompanying the shaded circles in the rightmost column. Perhaps relatedly, the mean estimate across filters correlates well with the behavioral data for the 200²⁰condition (top row, right-most column), and quite poorly for the 20020Dcondition (bottom row, right-most column).

The filled black circles indicate ongoing ITDRS estimates. First, while ongoing ITDRS does a poor job of predicting listener performance for the20020condition, it correlates quite well with the200^20D behavioral data. It would appear that the ITDRSfrom the initial portion of the stimulus is largely ignored in favor of an estimation based

on the accumulation of a succession of instances of ITDRS

that occur with narrowband amplitude fluctuations within and across filterbands. This ongoing ITDRSestimate pre- dicts the weak localization dominance observed in the behavioral data for the 4- and 5-ms lead/lag delay conditions, and is quite similar for both the200²⁰and200^20Dcondi- tions, as could, perhaps, be expected. Note that the construction of these two different stimuli used different portions of the same sample of noise, demonstrating that the model does not rely heavily on the particular noise sample that is used (see also [8]).

4. SUMMARY

These analyses suggest that ITDs extracted from rising en- velopes of neural output in response to both onset and ongoing stimulus portions may in fact explain the PE for long-duration noise stimuli. That is, it appears that no

“special” ongoing PE mechanism is required beyond that which already “falls out of” peripheral and brainstem processing. These basic peripheral mechanisms used to explain the PE for click stimuli, when combined with Dietz’s insight that ITDs appear to be extracted primarily from the rising slopes of the envelope of neural output, offer model outputs that correlate fairly closely with the data shown here. Though not shown here, the same model has been used to analyze other stimulus conditions, such as their

“quad” PE click-train stimuli, with similar correspondence between perceptual and modeling outcomes.

What this modeling cannot not explain is why there is onset dominance at the level of the entire stimulus. That is, why is the ITD estimate extracted from the beginning of

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the stimulus apparently weighted to a greater extent than ITD estimates extracted from subsequent stimulus portions? It may be that this onset dominance at the scale of the overall stimulus is the result of some adaptive neural response or chain of responses similar to those observed at the output of the auditory nerve. Future efforts will attempt to incorporate current physiological knowledge of neural responses, especially as they correlate with stimulus envelope, into a more complete model.

Also, the relation between modeling estimates and behavioral responses for stimulus conditions where the level of the lag is greater than that of the lead (see [9]). The purpose of these stimuli was to counteract the timing advantage of the lead with a level advantage for the lag so that the PE would “break down.” In analyzing how that

“break down” occurred, Pastore and Braasch hoped to un- derstand more about the mechanisms that underlie the PE.

Perhaps unsurprisingly, the relation between modeled ITD estimates, modeled ILDs, and listener performance be- come less clear and more complex. Additionally, variability within and between listeners also became highly variable. These issues are not considered here because they are not central to the basic idea that the PE may be studied using a conceptual framework of onset dominance at multiple time scales and levels of processing.

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