Masking of short tones in noise: Evidence for envelope-based, rather than energy-based detection

Abstract

The “temporal effect” in simultaneous masking may be characterized by better probe detection thresholds for a short, tonal probe presented at the temporal center of a masker compared to at the onset of a masker. Energy-based models of masking have been used to interpret the temporal effect as evidence that the gain of the auditory system decreases during acoustic stimulation. This study shows that masking from temporal-envelope fluctuations of a precursor or from a temporal gap between stimuli violates the assumptions of energy-based models and complicates the interpretation of temporal effects in terms of a reduction in gain. Detection thresholds were measured for a 6-ms, 4000-Hz probe preceded by a narrowband precursor and presented 2-, 197-, or 392-ms after the onset of a narrowband masker. The delay between the precursor offset and masker onset ranged from −2 to 250 ms. Probe thresholds were elevated in the presence of precursors with fluctuating compared to flattened temporal envelopes and when a temporal gap was inserted between the precursor and masker. The results suggest that the interpretation and design of temporal-effect studies should consider the masking effects of temporal-envelope fluctuations. These findings are consistent with speech-perception experiments that show masking from temporal-envelope fluctuations.

I. INTRODUCTION

Auditory masking experiments have been used to infer how the neural response of the auditory system changes over the duration of acoustic stimulation (Jesteadt et al., 1982; Champlin and McFadden, 1989; Roverud and Strickland, 2010). In simultaneous masking, these inferences are often made by comparing detection thresholds for short probes (e.g., < 20 ms) presented at different temporal locations within a longer masker (e.g., > 200 ms). The term “temporal effect” has been used to describe better detection thresholds for a short tonal probe presented at the temporal center of a longer masker, compared to thresholds for the same probe presented near the masker's onset (Wright, 1997). Temporal effects have been interpreted as evidence that the neural response of the auditory system adjusts in real-time over the forward fringe of the masker and that such adjustments improve sensitivity in auditory tasks (Smith and Zwislocki, 1975; Jennings et al., 2011). Several mechanisms have been identified as potential physiological correlates of temporal effects, such as the medial olivocochlear (MOC) reflex (Schmidt and Zwicker, 1991; von Klitzing and Kohlrausch, 1994; Strickland, 2001), classic-firing-rate adaptation in auditory nerve (AN) fibers (Smith and Zwislocki, 1975; Bacon and Takahashi, 1992), and dynamic-range adaptation of neurons in the AN or inferior colliculus (IC) (Marrufo-Perez et al., 2018; Marrufo-Perez et al., 2019). These mechanisms share common processing attributes in that they are elicited by acoustic stimuli, act as automatic gain control systems, and help improve the neural signal-to-noise ratio (SNR) of the response to the probe and masker (Liberman and Guinan, 1998). Classic-firing-rate adaptation decreases the response of the AN to a long-duration pedestal, while the response to a brief increment is constant regardless of the position of the increment within the pedestal, thus improving neural SNR for increments delayed from the onset of the pedestal (Smith and Zwislocki, 1975). Dynamic-range adaptation, which has a time constant on the order of 100–400 ms (AN) (Wen et al., 2009) or 3.2 s (IC) (Dean et al., 2005), results in a shift in the rate-level function toward improved neural coding of changes in intensity. This time dependent improvement in coding is expected to result in better detection thresholds for probes presented after dynamic-range adaptation has stabilized (i.e., when the probe is delayed from the onset of the masker) (Marrufo-Perez et al., 2019). Jennings et al. (2011) evaluated classic-firing-rate adaptation, dynamic-range adaptation, and MOC feedback as mechanisms of the temporal effect using a computational model of the auditory system. They found that classic-firing-rate adaptation and dynamic-range adaptation in AN fibers could not account for temporal effects measured with broadband noise (BBN) maskers in adults with normal hearing and cochlear hearing loss. Conversely, model results that included simulation of the MOC reflex predicted a temporal effect that was larger in adults with normal hearing compared to those with cochlear hearing loss, consistent with previous masking studies (Strickland, 2004; Strickland and Krishnan, 2005). In addition to these simulations, the dependence of the temporal effect on (1) masker intensity (Bacon, 1990), (2) ingestion of aspirin (McFadden and Champlin, 1990), (3) temporary threshold shifts (Champlin and McFadden, 1989), and (4) permanent hearing loss (Bacon and Takahashi, 1992; Strickland and Krishnan, 2005; Jennings et al., 2016) is consistent with a mechanism that acts on the outer hair cells (OHCs), such as the MOC reflex.

The primary effect of eliciting the MOC reflex is a decrease in OHC motility, which results in a reduction in cochlear amplifier gain (Guinan, 2006). This reduction in gain is greatest for low-level sounds and decreases with increasing input level, according to the level-dependent gain of the OHCs (Robles and Ruggero, 2001). The influence of such a reduction in gain on neural responses to a probe presented with a masker depends on the relative power of the probe and masker at the output of a cochlear filter. When the SNR is positive, as is typical for measurement of the temporal effect with BBN maskers (Jennings et al., 2018), eliciting the MOC reflex decreases the cochlear response to the masker more than that of the probe, thus improving the effective SNR (Strickland, 2008). Due to the “sluggish” onset of the MOC reflex (Backus and Guinan, 2006) a reduction in cochlear gain improves the effective SNR for probes presented in the temporal center of the masker compared to those presented near the masker's onset. This improvement in effective SNR is consistent with the temporal effect.

The temporal effect measured using simultaneous masking can be reduced by presenting an acoustic stimulus (“precursor”) before the onset of the masker (Bacon and Healy, 2000; Bacon and Liu, 2000; Savel and Bacon, 2003a). The primary effect of the precursor is to improve detection thresholds for probes presented near the masker's onset, while having little effect on probes located near the temporal center of the masker. The degree to which a precursor reduces the temporal effect depends on the level, duration, and laterality of the precursor, as well as the precursor's time delay and spectrum relative to the masker and probe (Bacon and Healy, 2000; Bacon and Liu, 2000). For 4000 Hz probes and higher-frequency tonal maskers (e.g., 5400 Hz), a large reduction in the temporal effect occurs when the precursor's level and spectrum are similar to those of the masker, the precursor's duration is greater than 150 ms, and the delay between the precursor's offset and masker's onset is less than 25 ms (Bacon and Healy, 2000). Similarly, for 4000 Hz probes presented in BBN maskers, the temporal effect is decreased more for broadband precursors than for noise precursors containing only spectral components above (high-band precursor) or below (low-band precursor) the probe frequency (Bacon and Liu, 2000). Finally, narrowband noise (NBN) precursors have a qualitatively distinct influence on the temporal effect; namely, probe thresholds near the onset of the masker are poorer when NBN precursors are present than when these precursors are absent (Bacon and Liu, 2000). This results in an increase, rather than a decrease, in the size of the temporal effect.

Jennings et al. (2018) proposed that the inherent temporal fluctuations of NBN precursors and maskers might disrupt the cues used by subjects to detect a short probe. They measured the temporal effect for NBN maskers whose temporal envelopes were processed to reduce temporal fluctuations, resulting in “flattened” and “fluctuating” NBN maskers. Consistent with previous studies using fluctuating NBN maskers (Bacon and Smith, 1991; Carlyon and White, 1992), a “negative” temporal effect was observed. Such a temporal effect is characterized by poorer detection thresholds for probes presented at the temporal center of the masker, compared to those presented near the masker's onset. Conversely, Jennings et al. (2018) observed a positive temporal effect of approximately 7 dB for flattened NBN maskers, which is qualitatively consistent with the temporal effect observed with tonal (Bacon and Viemeister, 1985) and BBN (Zwicker, 1965) maskers. The influence of flattening the masker's temporal envelope was primarily to improve probe detection thresholds overall and secondarily to improve these thresholds more for probes presented at the temporal center, compared to those presented near the onset of the masker. The influence of temporal-envelope fluctuations on probe detection thresholds were well accounted (R² = 0.94) for by a model that assumed that thresholds were proportional to the alternating current (AC)-coupled envelope power of the combined precursor/masker stimulus. The authors concluded that listeners may rely on a temporal-envelope-based cue to detect the probe and that the inherent fluctuations of the NBN masker may disrupt this cue. These results are qualitatively similar to the effect of simultaneous (Bacon and Grantham, 1989) and forward (Wojtczak et al., 2011) modulation masking, given that the period of the inherent masker fluctuations was similar to the duration of the probe. The results of Jennings et al. (2018) add to the literature that shows that temporal-envelope fluctuations contribute to the masking of tones (Svec et al., 2013; Svec et al., 2015, 2016) and speech (Stone et al., 2012).

In many studies of the temporal effect [e.g., Bacon and Savel (2004) and Strickland (2004)] the detection process has been assumed or modeled to follow the power spectrum model of masking (Fletcher, 1940). Predictions from this model are based on the assumption that the probe is detected at a constant signal-to-masker ratio at the output of an auditory filter centered on the probe frequency. In other words, it is assumed that the power (or energy) of the stimulus is the primary cue used by listeners to detect the probe. This simple assumption has proven to be a powerful tool in unifying many aspects of masking, particularly those associated with frequency selectivity (Patterson, 1976; Glasberg and Moore, 2000). Despite this utility, models based on energy cues cannot account for experiments on informational masking (Watson, 2005) or profile analysis (Green, 1983). Moreover, several studies show that cues based on the acoustic temporal envelope better account for thresholds from some masking (Richards, 1992; Davidson et al., 2006) and wideband-noise, level-discrimination experiments (Richards and Carney, 2019) compared to cues based on energy. Envelope-based processing is at the center of a class of auditory models that effectively predict psychophysical data by simulating the output of a modulation filterbank (Dau et al., 1996; Dau et al., 1997; Ewert and Dau, 2000). In addition to accounting for aspects of simultaneous and forward masking, such models predict modulation detection thresholds and modulation masking (Jepsen and Dau, 2011). The current study adopted a single-channel, envelope-based detection framework to account for precursor effects in simultaneous masking that are inconsistent with gain-reduction mechanisms and are not predicted by the power spectrum model of masking. Such effects include higher probe-detection thresholds for precursors with fluctuating compared to flattened envelopes and higher probe-detection thresholds when a small temporal gap is inserted between the masker and precursor, compared to no gap. This study also evaluated the possibility that the onsets and offsets of the precursor/masker introduce temporal-envelope fluctuations that may contribute to elevated probe thresholds. The envelope-based detection framework is evaluated here by testing the hypothesis that probe-detection thresholds are proportional to the AC-coupled envelope power occurring in a temporal window preceding the probe (Jennings et al., 2018). To compare with the power spectrum model of masking (Fletcher, 1940), calculations of acoustic root-mean-square (RMS) power were obtained. A single-channel framework was selected because the spectra of all stimuli (precursor, masker, probe) were narrower than an equivalent rectangular bandwidth (ERB) centered on 4000 Hz.

II. METHODS

A. Subjects

Eight normal-hearing adult subjects (age 22–28 years; 2 male) participated in the study. All subjects had audiometric thresholds ≤20 dB Hearing Level bilaterally at octave frequencies between 250 and 8000 Hz (ANSI, 2004), and normal middle ear status, confirmed by otoscopic examination and tympanometry (226 Hz probe). Subjects were paid for their participation.

B. Stimuli and apparatus

The 4000-Hz probe was 6-ms in duration and was presented 2, 197, or 392 ms after the onset of the 400-ms masker. These delays represent conditions where the temporal envelope of the low-noise noise (LNN) masker is relatively flat (197-ms delay) or abruptly changes due to the masker's onset (2-ms delay) or offset (392-ms delay). The NBN masker was centered spectrally on the probe frequency and had a bandwidth of 228 Hz, which is 0.5 ERB for normal hearing adults (Glasberg and Moore, 1990). The masker was processed to minimize temporal-envelope fluctuations by iteratively (10 times) dividing filtered Gaussian noise (GN) by the Hilbert envelope to create LNN, as described by Kohlrausch et al. (1997). This processing reduced but did not eliminate these fluctuations. Bandpass filtering was included after each iteration to limit the noise bandwidth to 0.5 ERB. A 200-ms precursor with a flattened (LNN) or fluctuating (GN) temporal envelope was presented before the masker with the following delays between the precursor's offset and the masker's onset (hereafter Δt): −2, 0, 10, 25, 100, or 250 ms. The −2 ms delay allowed the precursor and masker to crossfade without a perceptual gap between the two stimuli. This range of Δt values was used under the assumption that forward masking from the precursor would likely decay by 250 ms, based on studies of forward masking in the audio-frequency domain (Jesteadt et al., 1982) and modulation domain (Wojtczak and Viemeister, 2005). The NBN precursor had the same spectrum as the masker (i.e., 0.5 ERB centered at 4000 Hz). The duration of the precursor, masker, and probe were selected to be consistent with previous studies on temporal effects in simultaneous masking (Bacon and Healy, 2000; Bacon and Liu, 2000; Strickland, 2008; Jennings et al., 2016). The crest factor of the GN precursor was 10.7 dB, and that of the LNN precursor and masker was 4.4 dB. The precursor had the same spectrum as the masker, and the masker and precursor were presented at 75 dB sound pressure level (SPL) RMS pressure. The probe, masker, and precursor were each gated on and off with 3-ms cos² ramps. All masker and precursor noises were uniquely generated¹ (i.e., frozen noise was not used). A schematic representation of the envelopes of the stimuli is presented in Fig. 1. Stimuli were created using matlab®-based (The MathWorks, Natick, MA) software (Bidelman et al., 2015). A LynxTWO-B (Lynx Studio Technology, Costa Mesa, CA) sound card (sampling rate, 44.1 kHz; 24-bit resolution) and a headphone buffer (Tucker-Davis-Technologies, HB7, Alachua, FL) were used to drive the right channel of EARTONE-5A (3 M, Minneapolis, MN) insert earphones.

FIG. 1.

Schematic representation of the temporal envelopes of the precursor, masker, and probe stimuli used in the experiment. Narrowband noise (NBN) maskers had flattened temporal envelopes. NBN precursors had flattened (top row) or fluctuating (bottom row) temporal envelopes. The delay between the precursor's offset and the masker's onset (Δt) was systematically varied. The 6-ms probe was presented 2, 197, or 392 ms after the masker's onset (columns).

C. Procedure

Subjects sat in a double-walled, sound-attenuating room while participating in the experiments. Probe level at threshold was estimated using a three-interval, three-alternative forced-choice task, with a 1-up, 2-down adaptive rule to converge on 70.7% correct detection (Levitt, 1971). The initial level of the probe was 6 dB above the masker level. The step size of the adaptive track was 5 dB for the first four reversals and 2 dB for the remaining eight reversals.² The threshold of each adaptive track was defined as the average level of the final eight reversals. Observation intervals were marked by lights and separated by 500 ms. Two intervals contained the precursor/masker (no-probe interval) and one randomly selected interval contained the precursor/masker and probe (probe interval). Subjects pushed a button on a keyboard to indicate the interval in which the probe was perceived and visual feedback followed to indicate a correct or incorrect response.

Subjects were familiarized with the experiment by measuring two thresholds each for probes delayed 197 ms from the masker's onset in conditions without a precursor, with a flattened precursor (Δt = −2 ms), and with a fluctuating precursor (Δt = 100 ms). Subjects were then trained by completing three adaptive tracks each for the probe delayed 2, 197, and 392 ms from the masker's onset in conditions without a precursor, with a fluctuating precursor (Δt = −2 ms), and with a flattened precursor (Δt = 100 ms). Stimuli for familiarization and training were selected to cover the range of probe delays, precursor delays, and precursor types (flattened, fluctuating) encountered during the experiment. Subjects typically completed both familiarization and training tasks in 1.5–2 h. Thresholds measured during familiarization and training were discarded.

For data collection, half of the subjects completed the no precursor conditions first, while the other half started with the precursor conditions. The order in which subjects completed the conditions within precursor/no precursor blocks was randomized. Thresholds from three adaptive tracks were obtained for each condition and averaged to compute the final threshold. If the standard deviation of these adaptive tracks exceeded 5 dB, an additional adaptive track was obtained and included in the average. An additional adaptive track was obtained four times, twice for one subject and once each for two other subjects. The first threshold measured during a data collection session served as a “warm-up” and was discarded.

D. Analyses

Statistical testing consisted of a repeated-measures analysis of variance (ANOVA) to test the main effects and interactions of probe delay (2, 197, 392 ms), Δt (−2, 0, 10, 25, 100, or 250 ms), and precursor type (fluctuating, flattened). Post hoc testing consisted of additional repeated-measures ANOVAs and t-tests. The additional ANOVAs were included to facilitate interpretation of a significant three-way interaction. Statistical significance was evaluated at α = 0.05 after correcting for multiple comparisons via Bonferroni's method.

E. Envelope power calculations

This study tested the hypothesis that detection thresholds for short probes in long, flattened maskers preceded by flattened or fluctuating precursors are proportional to the AC-coupled power of the temporal envelope in an observation window surrounding the probe. The AC-coupled envelope power was calculated (Fig. 2) for the no-probe interval of each experimental condition. This calculation consisted of (1) computing the envelope via half-wave rectification and low-pass filtering (1st-order Butterworth, cutoff = 150 Hz), (2) squaring the resulting waveform, (3) high-pass filtering to remove the DC component (4th-order Butterworth, cutoff = 5 Hz), (4) applying an exponential window (time constant = 200 ms) starting at the temporal center of the probe and extending backward in time, and (5) computing the standard deviation of the resulting waveform. Regression analysis was performed to test whether probe thresholds were correlated with the AC-coupled envelope power. The exponential window applied greater weight to precursor/masker fluctuations occurring near the probe, similar to weighting windows used for models of forward masking (Oxenham, 2001). Preliminary calculations of AC-coupled envelope power revealed that an exponential window resulted in higher correlation with the behavioral data compared to other window shapes (rectangular, triangular, Hanning). The 200-ms time constant was selected based on Jennings et al. (2018), who reported this time constant resulted in the best-fitting regression model for masking thresholds obtained with flattened and fluctuating maskers. Moreover, the 200-ms exponential window is consistent with the time constant for temporal integration among adults with normal hearing for tone frequencies between 2000 and 8000 Hz (Gerken et al., 1990). For comparison, AC-coupled envelope power calculations were modified from the steps listed above to compute the acoustic RMS power, which is the decision variable of the power spectrum model of masking (Fletcher, 1940). This modification involved omitting the high-pass filter stage and computing the mean rather than the standard deviation at the output of the exponential window.

FIG. 2.

Block diagram of the steps used to calculate the AC-coupled envelope power of the experimental stimuli. The envelope was extracted via rectification and low-pass filtering and then squared. A high-pass filter was then applied to remove the DC component of the extracted envelope. The AC-coupled envelope power was computed as the standard deviation of the high-pass filtered envelope within an exponential time window occurring just prior to the probe's onset.

III. RESULTS

A. Detection thresholds

Probe threshold as a function of the delay between the precursor's offset and the masker's onset (Δt) is plotted in Fig. 3 for fluctuating (open symbols) and flattened (closed symbols) precursors. The top, middle, and bottom panels correspond to 2- (circles), 197- (triangles), and 392-ms (diamonds) probe delays, respectively. For comparison, probe thresholds obtained without a precursor (± one standard error) are plotted as gray shaded rectangles (no precursor condition). Statistical analysis of detection thresholds in the presence of the precursor (precursor condition) revealed significant main effects of precursor type (F[1,7] = 439.9, p < 0.001) and probe position (F[1,7] = 82.1, p < 0.001), a significant two-way interaction of precursor type and probe position (F[2,14] = 48.0, p < 0.001), and a three-way interaction of precursor type, probe position, and Δt (F[10,70]= 2.8, p < 0.01). Post hoc testing on the main effects revealed that probe thresholds were significantly higher for fluctuating compared to flattened precursors (t[7] = 2.6, p < 0.001), and significantly higher for probes delayed by 2 ms, compared to 197 ms (t[7] = 4.0, p < 0.001) and 392 ms (t[7] = 4.7, p < 0.001). Post hoc testing on the precursor type × probe position interaction revealed significantly higher probe thresholds in the presence of fluctuating precursors compared to flattened precursors when the probe was delayed by 2 ms (t[7] = −12.3, p < 0.001) or 197 ms (t[7] = −6.7, p < 0.001), but not 392 ms (t[7] = −3.0, p > 0.05).

FIG. 3.

Mean detection thresholds for 4000 Hz, 6-ms probes plotted as a function of the delay between the precursor's offset and the masker's onset. Probes were presented 2 (top), 197 (middle), and 392 ms (bottom) after the onset of the narrowband noise (NBN) masker. Solid and open symbols represent flattened and fluctuating NBN precursors. The grey shaded area represents the mean ± one standard error of probe detection thresholds without the precursor. Error bars are one standard error of the mean. Arrows mark conditions referred to in Sec. IV.

To understand the three-way interaction, three separate ANOVAs were conducted on the data obtained with 2-, 197-, and 392-ms probe positions. This analysis revealed that the interaction between Δt and precursor type (fluctuating, flattened) was significant for the 2-ms probe position (F[5,35] = 5.0, p < 0.001), but not for the 197 or 392 ms probe positions. In other words, the difference between thresholds measured with fluctuating and flattened precursors depended on Δt for probes delayed by 2 ms, but not for probes delayed by 197- or 392-ms. Pairwise comparison of the difference in threshold between fluctuating and flattened precursors for the 2-ms probe position was conducted based on the a priori hypothesis that probe thresholds should depend on the AC-coupled envelope power in a temporal window preceding the probe. This hypothesis predicts that differences in probe thresholds between flattened and fluctuating precursors will be significantly larger when Δt = −2 ms than for other precursor-masker delays. Consistent with this hypothesis, the difference in threshold between flattened and fluctuating precursors was significantly larger for Δt = −2 ms, than for Δt = 0 ms (t[7] = −3.0, p < 0.01), Δt = 25 ms (t[7] = −3.1, p < 0.01), Δt = 100 ms (t[7] = −4.1, p < 0.01), and Δt = 250 ms (t[7] = −5.4, p < 0.001). This result is largely due to relatively better detection thresholds in the presence of flattened precursors for Δt = −2 ms than for other precursor delays.

B. Envelope power calculations

Probe detection thresholds were compared with the AC-coupled envelope power in an exponential time window preceding the probe. This was done by plotting envelope power as a function of Δt for the three probe positions, in the same format as Fig. 3. Comparison of Figs. 3 and 4 reveals that the effects of precursor fluctuation, probe position, and Δt are qualitatively similar for envelope power calculations and probe thresholds. Specifically, envelope power is higher for fluctuating compared to flattened precursors, and for probes delayed by 2 ms compared to 197 and 392 ms. Moreover, the difference in envelope power between flattened and fluctuating precursors diminishes with increasing probe delay and increasing Δt. Conversely, calculations based on RMS power (Fig. 5) could not explain the effect of precursor fluctuation, as these calculations were nearly identical for fluctuating and flattened precursors. A correlation analysis was conducted to quantitatively test the hypothesis that probe thresholds are associated with AC-coupled envelope power calculations (Fig. 6). Consistent with the hypothesis, the correlation analysis revealed that variance in envelope power accounts for 83% of the variance in probe thresholds.

FIG. 4.

AC-coupled envelope power calculations plotted as a function of the delay between the precursor's offset and the masker's onset, as in Fig. 3. Calculations are shown for probes presented 2 (top), 197 (middle), and 392 ms (bottom) after the onset of the narrowband noise (NBN) masker. Solid and open symbols represent flattened and fluctuating NBN precursors. Arrows mark conditions referred to in Sec. IV.

FIG. 5.

RMS power calculations plotted as a function of the delay between the precursor's offset and the masker's onset, as in Fig. 3. Calculations are shown for probes presented 2 (top), 197 (middle), and 392 ms (bottom) after the onset of the narrowband noise (NBN) masker. Solid and open symbols represent flattened and fluctuating NBN precursors.

FIG. 6.

(Color online) Scatter plot of probe detection thresholds and AC-coupled envelope power calculations. Solid and open symbols represent values obtained with flattened and fluctuating narrowband noise (NBN) precursors. Red, navy, and cyan colored symbols represent probes presented 2, 197, and 392 ms after the onset of the NBN masker. Triangles, circles, diamonds, squares, right-pointing triangles, and left-pointing triangles represent precursor-masker delays of −2, 0, 10, 25, 100, and 250 ms, respectively.

IV. DISCUSSION

In the current study, fluctuating precursors and the temporal gap between the flattened precursor and the masker resulted in masking that cannot be accounted for by energy-based models of masking. The power spectrum model of masking predicts that fluctuating and flattened NBN precursors with equal RMS power will produce the same amount of masking (Fig. 5). Moreover, the insertion of a temporal gap between the precursor and probe will result in a release from masking, rather than an increase, according to this model (Oxenham, 2001). These findings are consistent with the observation that energy-based models of masking are unable to account for certain masking effects observed with NBN maskers in previous reports. For example, Oxenham (1998) measured probe thresholds as a function of probe duration for a 6000-Hz sinusoid presented near the center of a longer noise masker. Improvements in probe detection threshold resulting from a tenfold increase in probe duration were smaller (∼2.5 dB) than predicted by energy-based models (10 dB) when the bandwidth of the noise masker was very narrow (60 Hz). Model simulations based on envelope power were better able to account for these data compared to several energy-based models. The author concluded that listeners may rely on envelope-based cues for detection of short probes in NBN maskers, while energy-based cues may determine thresholds for longer probes, and for short probes in BBN. Similar success of envelope-based cues in accounting for tone-in-NBN detection was reported in several previous studies [e.g., Richards (1992) and Mao and Carney (2015)].

Reliance on envelope-based cues to detect short probes presented in NBN maskers introduces the possibility of informational masking (Buss et al., 2006). For example, the average period of the temporal-envelope fluctuations of a NBN (e.g., bandwidth <500 Hz) masker centered on 4000 Hz is similar to the period of the temporal envelope of a short, 4000 Hz probe (e.g., 2–20 ms) (Savel and Bacon, 2003b). Thus, listeners may lack a “quality-difference cue” (Neff, 1985) to identify the temporal envelope of the probe from among the inherent temporal fluctuations of the simultaneous (Jennings et al., 2018) or forward (Svec et al., 2015, 2016) masker. This lack of a quality difference cue originates in the similarity between the temporal envelopes of the probe and masker, and may be a form of informational masking. Alternatively, the inherent temporal fluctuations may produce masking unrelated to informational masking or confusion effects. For example, if the probe is detected at the output of a modulation filterbank [e.g., Gallun and Hafter (2006)], the response to the masker's envelope may swamp the response to the probe, resulting in a “line-busy” effect (Moore and Glasberg, 1982). Thus, the probe may go undetected because the response to the probe is absent rather than a failure to segregate the suprathreshold responses of the probe and masker. This swamping explanation is similar to explanations of simultaneous masking in the audio-frequency domain where the masker and probe overlap spectrally [i.e., “energetic masking,” Pickles (1984)], except in this case the envelope spectra of the masker and probe overlap.

From a physiological perspective, greater masking with fluctuating compared to flattened NBN precursors is consistent with forward masking in the amplitude-modulation (AM) domain at the level of the IC. This is based on the observation that the presence of the probe introduces a brief modulation in the amplitude of the stimulus envelope and that detection of this modulation determines probe threshold. Wojtczak et al. (2011) showed that IC responses from awake rabbits could account for the influence of an AM forward masker on AM detection thresholds in humans. In their experiment, human subjects detected a 50-ms burst of 40-Hz AM presented within a 500-ms, 5500-Hz carrier. The probe AM was preceded by the unmodulated carrier, or by a 150-ms burst of AM (40 Hz, masker) at 100% modulation depth. The delay between the masker and probe AM ranged from 0 to 210 ms. AM detection thresholds were up to 15 dB poorer when masker AM preceded the probe, compared to no masker. AM detection thresholds improved exponentially as a function of masker-probe delay. Despite this recovery, AM detection thresholds measured with the AM masker remained poorer than those for the no-masker condition for all probe delays. The slow recovery from AM masking was predicted by responses of IC neurons in rabbits when IC firing rate was compared between analysis windows occurring immediately prior and immediately during the probe AM. In the current experiment, probe thresholds were elevated by up to 8–9 dB in the presence of fluctuating compared to flattened precursors for Δt = −2 ms and probe delay = 2 ms. This elevation is qualitatively similar to the elevation in AM detection thresholds in the presence of an AM masker at short masker-probe delays. Moreover, thresholds for probes delayed by 2 ms from the masker recovered slowly as a function of Δt for fluctuating precursors, which is consistent with the slow recovery of AM forward masking (Wojtczak and Viemeister, 2005). The time constant in the current study (200 ms) is longer than the ∼100 ms time constant reported in previous studies on forward masking of AM (Wojtczak and Viemeister, 2005; Wojtczak et al., 2011). A longer time constant was needed to account for the slow decay of masking for probes presented near the onset of the masker and in the presence of a fluctuating precursor (Fig. 3, open circles, top panel). As discussed below, this longer-than-expected time constant reveals an area of improvement for the framework presented in Fig. 2.

Although the AC-coupled power calculations captured the effects of precursor type and precursor-masker delay, these calculations failed to capture details of the complex interaction among precursor type, precursor-masker delay, and probe delay. For example, probe thresholds recovered more slowly than predicted by AC-coupled envelope power calculations when the probe was presented at the onset of the masker (2-ms delay) and in the presence of the fluctuating precursor (Fig. 3, open circles). These elevated thresholds may be due to the slow decay of the precursor's effective temporal envelope; however, additional masking from the masker's onset likely interacts with masking from precursor fluctuations. For example, the delay from the precursor's offset and the probe's onset is roughly equal (∼250 ms) for the following measurements: (1) the fluctuating precursor delayed by 250 ms from the masker's onset with a 2-ms, masker-probe delay (Fig. 3, open circle with arrow) and (2) the fluctuating precursor delayed by 25 ms with a 197-ms, masker-probe delay (Fig. 3 open triangle with arrow). Although these experimental conditions have similar delays between the precursor and probe, thresholds are nearly 5.5 dB higher when the probe is presented near the masker's onset. A similar, but smaller elevation in threshold (∼3 dB) exists when making the same comparison with flattened precursors. The AC-coupled envelope power calculations account for the main effect of precursor envelope fluctuation and how this effect decreases with increasing probe delay (Fig. 4). Despite this, these calculations do not predict the three-way interaction among precursor fluctuation, probe delay, and precursor-masker delay. This interaction is responsible for the greater masking produced by probes presented at the masker's onset for fluctuating precursors with roughly equal precursor-probe delays (Figs. 3 and 4, arrows). This indicates that the envelope-based decision framework, as embodied in Fig. 2, lacks a conceptual element that models this three-way interaction. Candidate physiological mechanisms to describe this interaction may involve sensitization to the onset of a stimulus (e.g., masker) that follows a preceding stimulus with a fluctuating envelope (e.g., precursor). Currently, it is unclear what physiological mechanisms demonstrate such properties.

Although envelope fluctuations from the precursor and from the onset of the masker are responsible for much of the masking not accounted for by energy, the temporal gap between the precursor and masker also contributes to this masking. Probe thresholds, in the presence of flattened precursors, increased and then decreased as the precursor-masker delay increased from −2 to 25 ms for probes presented at 2 and 197 ms after the masker's onset (Fig. 3, filled symbols, top and middle panels). The increase in probe thresholds ranged between 1.5 dB (197-ms probe delay) to 3 dB (2-ms probe delay). The AC-coupled power calculations qualitatively capture this increase, then decrease in probe thresholds (Fig. 4, filled symbols, top and middle panels); however, the delay marking the transition between increasing to decreasing probe thresholds is later (∼25 ms) than observed for the empirical data (0–10 ms). For a −2 ms precursor-masker delay, the AC-envelope power is relatively low because the flattened precursor and masker ramps are crossfaded, which eliminates a temporal gap. As the precursor-masker delay is increased, a temporal gap is introduced. The offset of the precursor and onset of the masker marking this gap contribute to the AC-coupled envelope power if these offset/onset events are near the peak of the exponential window. As the precursor-masker delay is increased further, the offset of the precursor falls within the tail of the exponential window and therefore contributes little to the AC-coupled power calculation. The framework for these calculations (Fig. 2), in particular the weighting window, may need to be updated in future studies to account for the precursor-masker delay producing the highest probe thresholds when the flattened precursor is presented. Similarly, another future update to the framework may involve simulating detection thresholds using a signal-detection-theory approach that considers the probe's envelope spectrum in addition to the envelope spectra of the precursor and masker. Such an update may be useful in evaluating prospective mechanisms for modulation masking such as masker-target similarity and swamping in the envelope domain. The AC-coupled power calculations represent a simplified version of modulation-domain models that have been published previously [e.g., Dau et al. (1996)]. This simplification involved calculating envelope power over a wide bandwidth, rather than at the output of several modulation filters. These AC-coupled power calculations represent an initial attempt to account for the effects of precursor/masker fluctuation on temporal effects in simultaneous masking using a modulation-domain model.

The findings from the current experiment have implications for interpreting results from previous and future studies on the temporal effect, particularly studies that include NBN precursors/maskers (Bacon and Smith, 1991; Carlyon and White, 1992) and temporal gaps between stimuli (McFadden, 1989; Roverud and Strickland, 2010). The majority of studies on the temporal effect use short-duration probes [< 30 ms, e.g., Bacon (1990), McFadden and Champlin (1990), Wright (1997), Strickland (2001), and Jennings et al. (2016)]. When precursor fluctuations or temporal gaps between stimuli have similar periods as these short-duration probes, a masking effect occurs that violates the assumptions of the power-spectrum model of masking. This complicates the interpretation of studies of the temporal effect that tested hypotheses centered on the influence of gain control mechanisms such as the MOC reflex, auditory-nerve adaptation, or dynamic-range adaptation. Simulations from auditory models that extend the power-spectrum model to account for the effects of envelope fluctuations on detection thresholds (Dau et al., 1997; Carney, 2018) are likely to avoid such complications. Moreover, such models are likely to account for the temporal effect if simulation of the MOC reflex is included in the model architecture. Simulation of the MOC reflex reduces the post-cochlear output of the lower-level masker more than that of the higher-level probe (Strickland, 2008); thus, improving the effective SNR at the input to model stages that account for envelope processing (e.g., modulation filterbank). Future experiments on the temporal effect may benefit from the use of such models, and may reduce the masking effects of fluctuating precursors/temporal gaps by (1) avoiding precursors that include slow temporal fluctuations that are on the same temporal order as the duration of the probe which can cause an elevation in probe threshold as seen in this experiment between flattened and fluctuating precursors (Fig. 3, top panel), and (2) avoiding the insertion of temporal gaps between stimuli (precursors, maskers, probes), including the temporal gaps created by offset and onset ramps which can also elevate probe thresholds as seen in Fig. 3 (top panel) when comparing between the −2 and 0 ms delay conditions for a flattened precursor. One method for avoiding temporal gaps is to crossfade the ramps of stimuli [e.g., Jennings et al. (2018)].

Gain-control mechanisms are unlikely to contribute to the results of the current experiment and those from a recent experiment (Jennings et al., 2018) that provided the motivation for this study. Such mechanisms are invoked to explain temporal effects in simultaneous masking, whereby sensitivity to a probe presented at the onset of a longer masker (e.g., 500 ms) is improved by presenting a precursor, or by moving the probe toward the temporal center of the masker. In the current study, probe thresholds increased or remained constant when a precursor was present, except for the presentation of a flattened precursor with a −2 ms precursor-masker delay [Fig. 3, top panel, compare gray shaded area (no-precursor condition) with the first filled circle]. A similar improvement (approximately 3 dB) in probe threshold was observed for probes delayed by 197 ms, compared to 2 ms, from the onset of the masker in the no-precursor condition (Fig. 3, compare shaded areas between the top and middle panels). As discussed by Jennings et al. (2018), temporal effects for flattened NBN maskers/precursors are inconsistent with those measured with BBN maskers/precursors, which have been modeled as a reduction in cochlear gain (Jennings et al., 2011; Jennings et al., 2016). This inconsistency was illustrated (their Fig. 5) by differences in the slope of growth of masking between BBN and NBN maskers. For BBN maskers, the slope of growth of masking is shallow (<1 dB/dB) when the probe occurs at the onset of the masker and is preceded by silence, whereas the slope approaches 1 dB/dB when the probe is preceded by a BBN precursor or forward fringe of the BBN masker. This change in slope is consistent with a decrease in cochlear nonlinearity (Oxenham and Plack, 1997; Bacon et al., 1999). For NBN maskers, the growth of masking slope approaches 1 dB/dB and is expansive (> 1 dB/dB) when the probe is preceded by silence or acoustic stimulation (masker/precursor), respectively. Such a change in slope is inconsistent with a reduction in cochlear gain, suggesting other mechanisms are responsible for temporal effects observed with flattened NBN maskers/precursors. The hypothesis that temporal effects result from more than one mechanism has been reported previously (Carlyon and White, 1992; Bacon and Savel, 2004). Although these conclusions encourage caution when interpreting temporal effects, they do not imply that gain-control mechanisms cannot be responsible for the temporal effects reported in other studies. For example, the influence of temporary threshold shift (Champlin and McFadden, 1989), aspirin ingestion (McFadden and Champlin, 1990), cochlear hearing loss (Bacon and Takahashi, 1992), probe/masker level (Bacon, 1990), and probe/masker phase (von Klitzing and Kohlrausch, 1994) on temporal effects are difficult to explain without invoking mechanisms that reduce gain.

Maskers in ecological listening scenarios often have fluctuating temporal envelopes. For example, the temporal envelope of a speech masker fluctuates during and between vocalizations according to the movement of the vocal tract. Results from this study are consistent with the notion that these inherent masker envelope fluctuations are a source of masking beyond that which is accounted for by energy alone (Stone et al., 2012). Moreover, the current experiment reveals that this modulation masking has an appreciable forward masking component. Although not tested here, it is likely this forward masking component depends on the similarity among the precursor/masker and target modulation spectra. For example, Savel and Bacon (2003 b) showed that fluctuating NBN maskers produce more simultaneous masking than tonal maskers for short probes (10 ms), but not for longer probes (200 ms). The average period of the inherent fluctuations of their NBN masker was 6.2 ms, which is similar to the duration of the short probe, thus resulting in overlapping envelope spectra between the masker and probe. The envelope spectra of their NBN masker and 200-ms probe are expected to have less overlap consistent with a release from modulation masking. Similar results have been reported in speech-on-speech masking experiments (Fogerty et al., 2016), where a change in the masker's envelope spectrum via time compression resulted in better keyword identification than when the envelope spectra between masker and target speech were similar (no time compression).

V. CONCLUSIONS

Slow fluctuations in the acoustic envelope of stimuli used to study the temporal effect result in masking that is not predicted by traditional energy-based models. These fluctuations can originate in the inherent temporal fluctuations of NBN precursor and maskers, or from temporal gaps inserted between stimuli. The interpretation of the temporal effect in terms of physiological mechanisms that automatically adjust gain is complicated by these envelope masking effects. Such masking effects can be avoided in future studies by including envelope-based model simulations and by carefully designing experimental stimuli to avoid envelope fluctuations that are on the same order as the period of the probe's envelope.