Binaural processing of modulated interaural level differences

Two experiments are presented that measure the acuity of binaural processing of modulated interaural level differences (ILDs) using psychoacoustic methods. In both experiments, dynamic ILDs were created by imposing an interaurally antiphasic sinusoidal amplitude modulation (AM) signal on high-frequency carriers, which were presented over headphones. In the first experiment, the sensitivity to dynamic ILDs was measured as a function of the modulation frequency using puretone, and interaurally correlated and uncorrelated narrow-band noise carriers. The intrinsic interaural level fluctuations of the uncorrelated noise carriers raised the ILD modulation detection thresholds with respect to the pure-tone carriers. The diotic fluctuations of the correlated noise carriers also caused a small increase in the thresholds over the pure-tone carriers, particularly with low ILD modulation frequencies. The second experiment investigated the modulation frequency selectivity in dynamic ILD processing by imposing an interaurally uncorrelated bandpass noise AM masker in series with the interaurally antiphasic AM signal on a pure-tone carrier. By varying the masker center frequencies relative to the signal modulation frequency, broadly tuned, bandpass-shaped patterns were obtained. Simulations with an existing binaural model show that a low-pass filter to limit the binaural temporal resolution is not sufficient to predict the results of the experiments.     

Spectral modulation detection as a function of modulation frequency, carrier bandwidth, and carrier frequency region

The present study investigates the nature of spectral envelope perception using a spectral modulation detection task in which sinusoidal spectral modulation is superimposed upon a noise carrier. The principal goal of this study is to characterize spectral envelope perception in terms of the influence of modulation frequency (cycles/octave), carrier bandwidth (octaves), and carrier frequency region (defined by lower and upper cutoff frequencies in Hz). Spectral modulation detection thresholds measured as a function of spectral modulation frequency result in a spectral modulation transfer function (SMTF). The general form of the SMTF is bandpass in nature, with a minimum modulation detection threshold in the region between 2 to 4 cycles/octave. SMTFs are not strongly dependent on carrier bandwidth (ranging from 1 to 6 octaves) or carrier frequency region (ranging from 200 to 12 800 Hz), with the exception of carrier bands restricted to very low audio frequencies (e.g., 200-400 Hz). Spectral modulation detection thresholds do not depend on the presence of random level variations or random modulation phase across intervals. The SMTFs reported here and associated excitation pattern computations are considered in terms of a linear systems approach to spectral envelope perception and potential underlying mechanisms for the perception of spectral features.     

An analysis of quasi-frequency-modulated noise and random-sideband noise as comparisons for amplitude-modulated noise

Experiments were performed to determine under what conditions quasi-frequency-modulated (QFM) noise and random-sideband noise are suitable comparisons for AM noise in measuring a temporal modulation transfer function (TMTF). Thresholds were measured for discrimination of QFM from random-sideband noise and AM from QFM noise as a function of sideband separation. In the first experiment, the upper spectral edge of the noise stimuli was at 2400 Hz and the bandwidth was 1600 Hz. For sideband separations up to 256 Hz, at threshold sideband levels for discriminating AM from QFM noise, QFM was indiscriminable from random-sideband noise. For the largest sideband separation used (512 Hz), listeners may have used within-stimulus envelope correlation in the QFM noise to discriminate it from the random-sideband noise. Results when stimulus bandwidth was varied suggest that listeners were able to use this cue when the carrier was wider than a critical band, and the sideband separation approached the carrier bandwidth. Within-stimulus envelope correlation was also present in AM noise, and thus QFM noise was a suitable comparison because it made this cue unusable and forced listeners to use across-stimulus envelope differences. When the carrier bandwidth was less than a critical band or was wideband, QFM noise and random-sideband noise were equally suitable comparisons for AM noise. When discrimination thresholds for QFM and random-sideband noise were converted to modulation depth and modulation frequency, they were nearly identical to those for discrimination of AM from QFM noise, suggesting that listeners were using amplitude modulation cues in both cases.     

Within- versus cross-channel mechanisms in detection of envelope phase disparity

These experiments were designed to examine the mechanism of detection of phase disparity in the envelopes of two sinusoidally amplitude-modulated (AM) sinusoids. Specifically, they were performed to determine whether detection of envelope phase disparity was consistent with processing within a single channel in which the AM tones were simply added. In the first condition, with an 8-Hz modulation frequency, phase-disparity thresholds increased sharply with an initial increase in separation of the carrier frequencies. They then remained approximately constant when the separation was an octave or above. In the second condition, with carrier pairs of 1 and 2 kHz or 1 and 3.2 kHz and a modulation frequency of 8 Hz, thresholds were little affected as the level of one carrier was decreased relative to the other. With a modulation frequency of 128 Hz, for most subjects there was more of an effect of level disparity on thresholds. In the third condition, when the modulation frequency was 8 Hz, subjects showed relatively constant thresholds whether the signals were presented monotically, dichotically, or dichotically with low- and high-pass noise. Dichotic thresholds were typically higher than monotic when the modulation frequency was 128 Hz. These results suggest that it is not necessary to have information available within a single additive channel to detect envelope phase disparity. In certain circumstances, a comparison across channels may be used to detect such disparities.     

External and internal limitations in amplitude-modulation processing

Three experiments are presented to explore the relative role of "external" signal variability and "internal" resolution limitations of the auditory system in the detection and discrimination of amplitude modulations (AM). In the first experiment, AM-depth discrimination performance was determined using sinusoidally modulated broadband-noise and pure-tone carriers. The AM index, m, of the standard ranged from -28 to -3 dB (expressed as 20 log m). AM-depth discrimination thresholds were found to be a fraction of the AM depth of the standard for standards down to -18 dB, in the case of the pure-tone carrier, and down to -8 dB, in the case of the broadband-noise carrier. For smaller standards, AM-depth discrimination required a fixed increase in AM depth, independent of the AM depth of the standard. In the second experiment, AM-detection thresholds were obtained for signal-modulation frequencies of 4, 16, 64, and 256 Hz, applied to either a band-limited random-noise carrier or a deterministic ("frozen") noise carrier, as a function of carrier bandwidth (8 to 2048 Hz). In general, detection thresholds were higher for the random- than for the frozen-noise carriers. For both carrier types, thresholds followed the pattern expected from frequency-selective processing of the stimulus envelope. The third experiment investigated AM masking at 4, 16, and 64 Hz in the presence of a narrow-band masker modulation. The variability of the masker was changed from entirely frozen to entirely random, while the long-term average envelope power spectrum was held constant. The experiment examined the validity of a long-term average quantity as the decision variable, and the role of memory in experiments with frozen-noise maskers. The empirical results were compared to predictions obtained with two modulation-filterbank models. The predictions revealed that AM-depth discrimination and AM detection are limited by a combination of the external signal variability and an internal "Weber-fraction" noise process.     

The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers

This paper is concerned with modulation and beat detection for sinusoidal carriers. In the first experiment, temporal modulation transfer functions (TMTFs) were measured for carrier frequencies between 1 and 10 kHz. Modulation rates covered the range from 10 Hz to about the rate equaling the critical bandwidth at the carrier frequency. In experiment 2, TMTFs for three carrier frequencies were obtained as a function of the carrier level. In the final experiment, thresholds for the detection of either the lower or the upper modulation sideband (beat detection) were measured for "carrier" frequencies of 5 and 10 kHz, using the same range of modulation rates as in experiment 1. The TMTFs for carrier frequencies of 2 kHz and higher remained flat up to a modulation rate of about 100-130 Hz and had similar values across carrier frequencies. For higher rates, modulation thresholds initially increased and then decreased rapidly, reflecting the subjects' ability to resolve the sidebands spectrally. Detection thresholds generally improved with increasing carrier level, but large variations in the exact level dependence were observed, across subjects as well as across carrier frequencies. For beat rates up to about 70 Hz (at 5 kHz) and 100 Hz (at 10 kHz), beat detection thresholds were the same for the upper and the lower sidebands and were about 6 dB higher than the level per sideband at the modulation-detection threshold. At higher rates the threshold for both sidebands increased, but the increase was larger for the lower sideband. This reflects an asymmetry in masking with more masking towards lower frequencies. Only at rates well beyond the maximum of the TMTF did detection for the lower sideband start to be better than that for the upper sideband. The asymmetry at intermediate frequency separations can be explained by assuming that detection always takes place in filters centered above the stimulus spectrum. The shape of the TMTF and the beat-detection data reflects a limitation in resolving fast amplitude variations, which must occur central to the inner-ear filtering. Its characteristic resembles that of a first-order low-pass filter with a cutoff frequency of about 150 Hz.     

Spectro-temporal processing in the envelope-frequency domain

The frequency selectivity for amplitude modulation applied to tonal carriers and the role of beats between modulators in modulation masking were studied. Beats between the masker and signal modulation as well as intrinsic envelope fluctuations of narrow-band-noise modulators are characterized by fluctuations in the "second-order" envelope (referred to as the "venelope" in the following). In experiment 1, masked threshold patterns (MTPs), representing signal modulation threshold as a function of masker-modulation frequency, were obtained for signal-modulation frequencies of 4, 16, and 64 Hz in the presence of a narrow-band-noise masker modulation, both applied to the same sinusoidal carrier. Carrier frequencies of 1.4, 2.8, and 5.5 kHz were used. The shape and relative bandwidth of the MTPs were found to be independent of the signal-modulation frequency and the carrier frequency. Experiment 2 investigated the extent to which the detection of beats between signal and masker modulation is involved in tone-in-noise (TN), noise-in-tone (NT), and tone-in-tone (TT) modulation masking, whereby the TN condition was similar to the one used in the first experiment. A signal-modulation frequency of 64 Hz, applied to a 2.8-kHz carrier, was tested. Thresholds in the NT condition were always lower than in the TN condition, analogous to the masking effects known from corresponding experiments in the audio-frequency domain. TT masking conditions generally produced the lowest thresholds and were strongly influenced by the detection of beats between the signal and the masker modulation. In experiment 3, TT masked-threshold patterns were obtained in the presence of an additional sinusoidal masker at the beat frequency. Signal-modulation frequencies of 32, 64, and 128 Hz, applied to a 2.8-kHz carrier, were used. It was found that the presence of an additional modulation at the beat frequency hampered the subject's ability to detect the envelope beats and raised thresholds up to a level comparable to that found in the TN condition. The results of the current study suggest that (i) venelope fluctuations play a similar role in modulation masking as envelope fluctuations do in spectral masking, and (ii) envelope and venelope fluctuations are processed by a common mechanism. To interpret the empirical findings, a general model structure for the processing of envelope and venelope fluctuations is proposed.     

A comparison of steady-state evoked potentials to modulated tones in awake and sleeping humans.

Steady-state evoked potential responses were measured to binaural amplitude-modulated (AM) and combined amplitude- and frequency-modulated (AM/FM) tones. For awake subjects, AM/FM tones produced larger amplitude responses than did AM tones. Awake and sleeping responses to 30-dB HL AM/FM tones were compared. Response amplitudes were lower during sleep and the extent to which they differed from awake amplitudes was dependent on both carrier and modulation frequencies. Background EEG noise at the stimulus modulation frequency was also reduced during sleep and varied with modulation frequency. A detection efficiency function was used to indicate the modulation frequencies likely to be most suitable for electrical estimation of behavioral threshold. In awake subjects, for all carrier frequencies tested, detection efficiency was highest at a modulation frequency of 45 Hz. In sleeping subjects, the modulation frequency regions of highest efficiency varied with carrier frequency. For carrier frequencies of 250 Hz, 500 Hz, and 1 kHz, the highest efficiencies were found in two modulation frequency regions centered on 45 and 90 Hz. For 2 and 4 kHz, the highest efficiencies were at modulation frequencies above 70 Hz. Sleep stage affected both response amplitude and background EEG noise in a manner that depended on modulation frequency. The results of this study suggest that, for sleeping subjects, modulation frequencies above 70 Hz may be best when using steady-state potentials for hearing threshold estimation.     

Critical modulation frequency based on detection of AM versus FM tones

The ratios between the modulation index (eta) for just noticeable FM of a sinusoidally modulated pure tone and the degree of modulation (m) for just noticeable AM at the same carrier and the same modulation frequency were measured at carrier frequencies of 0.125, 0.25, 0.5, 1, 2, 4, and 8 kHz. Signal levels were 20 dB SL and 50 dB SPL or 80 dB SPL. At low modulation frequencies, for example, 8 Hz, AM and FM elicit very different auditory sensations (i.e., a fluctuation in loudness or pitch, respectively). In this case, eta and m show different values for just noticeable modulation. Since both stimuli have almost equal amplitude spectra if eta equals m (m less than 0.3), the difference in detection thresholds reflects differences in the phase relation between carrier and sidebands in AM and FM. With increasing modulation frequency, the eta-m ratio decreases and reaches unity at a modulation frequency called the "critical modulation frequency" (CMF). At modulation frequencies above the CMF, the same modulation thresholds are obtained for AM and FM. Therefore, it can be concluded that the difference in phase between the two types of stimuli is not perceived in this range. At center frequencies below 1 kHz, where phase errors caused by headphones and ear canal presumably are small, the CMF is useful in estimating critical bandwidth.     

Second-order temporal modulation transfer functions

Detection thresholds were measured for a sinusoidal modulation applied to the modulation depth of a sinusoidally amplitude-modulated (SAM) white noise carrier as a function of the frequency of the modulation applied to the modulation depth (referred to as f'm). The SAM noise acted therefore as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM-noise modulation depth generated two additional components in the modulation spectrum: fm-f'm and fm+f'm. The tracking variable was the modulation depth of the sinusoidal variation applied to the "carrier" modulation depth. The resulting "second-order" temporal modulation transfer functions (TMTFs) measured on four listeners for "carrier" modulation frequencies fm of 16, 64, and 256 Hz display a low-pass segment followed by a plateau. This indicates that sensitivity to fluctuations in the strength of amplitude modulation is best for fluctuation rates f'm below about 2-4 Hz when using broadband noise carriers. Measurements of masked modulation detection thresholds for the lower and upper modulation sideband suggest that this capacity is possibly related to the detection of a beat in the sound's temporal envelope. The results appear qualitatively consistent with the predictions of an envelope detector model consisting of a low-pass filtering stage followed by a decision stage. Unlike listeners' performance, a modulation filterbank model using Q values > or = 2 should predict that second-order modulation detection thresholds should decrease at high values of f'm due to the spectral resolution of the modulation sidebands (in the modulation domain). This suggests that, if such modulation filters do exist, their selectivity is poor. In the latter case, the Q value of modulation filters would have to be less than 2. This estimate of modulation filter selectivity is consistent with the results of a previous study using a modulation-masking paradigm [S. D. Ewert and T. Dau, J. Acoust. Soc. Am. 108, 1181-1196 (2000)].     

The role of frequency selectivity in measures of auditory and vibrotactile temporal resolution.

The purpose of this study was to compare the role of frequency selectivity in measures of auditory and vibrotactile temporal resolution. In the first experiment, temporal modulation transfer functions for a sinusoidally amplitude modulated (SAM) 250-Hz carrier revealed auditory modulation thresholds significantly lower than corresponding vibrotactile modulation thresholds at SAM frequencies greater than or equal to 100 Hz. In the second experiment, auditory and vibrotactile gap detection thresholds were measured by presenting silent gaps bounded by markers of the same or different frequency. The marker frequency F1 = 250 Hz preceded the silent gap and marker frequencies after the silent gap included F2 = 250, 255, 263, 310, and 325 Hz. Auditory gap detection thresholds were lower than corresponding vibrotactile thresholds for F2 markers less than or equal to 263 Hz, but were greater than the corresponding vibrotactile gap detection thresholds for F2 markers greater than or equal to 310 Hz. When the auditory gap detection thresholds were transformed into filter attenuation values, the results were modeled well by a constant-percentage (10%) bandwidth filter centered on F1. The vibrotactile gap detection thresholds, however, were independent of marker frequency separation. In a third experiment, auditory and vibrotactile rate difference limens (RDLs) were measured for a 250-Hz carrier at SAM rates less than or equal to 100 Hz. Auditory RDLs were lower than corresponding vibrotactile RDLs for standard rates greater than 10 Hz. Combination tones may have confounded auditory performance for standard rates of 80 and 100 Hz. The results from these experiments revealed that frequency selectivity influences auditory measures of temporal resolution, but there was no evidence of frequency selectivity affecting vibrotactile temporal resolution.     

Modeling the influence of inherent envelope fluctuations in simultaneous masking experiments

Masked thresholds are measured and simulated for bandpass-noise signals ranging in bandwidth from 4 to 256 Hz in the presence of a masking bandpass noise also ranging in bandwidth from 4 to 256 Hz. Signal and masker are centered at 2 kHz. To investigate the role of temporal processing in simultaneous masking, simulations were performed with the modulation-filterbank model by Dau et al. [J. Acoust. Soc Am. 102, 2906-2919 (1997)]. For a fixed masker bandwidth, thresholds are independent of the signal bandwidth as long as the signal bandwidth does not exceed the masker bandwidth and thresholds decrease with increasing masker bandwidth in those conditions. A simple modulation-low-pass filter (energy integrator) would be sufficient to describe the experimental results in those conditions. In contrast, the processing by a modulation filterbank is necessary to account for the conditions of "asymmetry of masking," where thresholds for signals with bandwidths larger than the masker bandwidth are much lower than those for the reversed condition. In those conditions, the modulation-filterbank model is able to use the inherent higher modulation frequencies of the signal as an additional cue.     

The range of spectral integration.

The results of two complementary detection tasks using digitally synthesized noise are reported. In one experiment the bandwidth of the synthetic noise was varied to reveal the region most effective in masking a 1-kHz signal. The bandwidth of the internal filter ("critical band") so measured was about 80 Hz. In another experiment, a wideband noise was used as the masker for a synthetic signal whose bandwidth another experiment, a wideband noise was used as the masker for a synthetic signal whose bandwidth was varied to determine the maximum effective width of the internal filter. Although some earlier experiments suggest maximum effective widths as small as 180-200 Hz (around 1 kHz), the data reported here indicate the range of spectral integration extends from the critical band to a maximum width that may exceed 3 kHz. In addition, the good agreement between the two experiments suggests a new method for estimating critical bandwidths based on the determination of two thresholds: that of a tonal signal in a wideband masker and that of a supracritical-width noise signal in a wider-bandwidth masker.     

Modulation masking: effects of modulation frequency, depth, and phase

Modulation thresholds were measured for a sinusoidally amplitude-modulated (SAM) broadband noise in the presence of a SAM broadband background noise with a modulation depth (mm) of 0.00, 0.25, or 0.50, where the condition mm = 0.00 corresponds to standard (unmasked) modulation detection. The modulation frequency of the masker was 4, 16, or 64 Hz; the modulation frequency of the signal ranged from 2-512 Hz. The greatest amount of modulation masking (masked threshold minus unmasked threshold) typically occurred when the signal frequency was near the masker frequency. The modulation masking patterns (amount of modulation masking versus signal frequency) for the 4-Hz masker were low pass, whereas the patterns for the 16- and 64-Hz maskers were somewhat bandpass (although not strictly so). In general, the greater the modulation depth of the masker, the greater the amount of modulation masking (although this trend was reversed for the 4-Hz masker at high signal frequencies). These modulation-masking data suggest that there are channels in the auditory system which are tuned for the detection of modulation frequency, much like there are channels (critical bands or auditory filters) tuned for the detection of spectral frequency.     

包络调制率和载波频率对听觉时间调制检测能力的影响

通过心理物理实验探讨了包络调制率(<300 Hz)和纯音载波频率(<8 kHz)对听觉时间调制检测能力的影响. 测试信号为以纯音为载波的正弦幅度调制信号, 采用二选一强迫选择法和自适应调整步长的心理物理实验方法, 测试得到不同载波频率条件下的时间调制传递函数. 实验结果表明, 包络调制率和载波频率均会对听觉的时间调制检测能力产生影响. 当载波频率低于2 kHz时, 人耳的检测能力与调制率呈单调递增趋势;当载波频率高于3.5 kHz时, 检测能力也会受到调制率的显著影响, 但没有显著的单调变化趋势. 当调制率在10-100 Hz之间时, 检测能力不随载波频率明显变化;当调制率在150-300 Hz之间时, 调制检测能力随着载波频率上升而下降, 在载波频率达到3.5 kHz时, 调制检测能力不随载波频率显著改变.     

Detection of modulation of a 4-kHz carrier

To better understand the processing of complex high-frequency sounds, modulation-detection thresholds were measured for sinusoidal frequency modulation (SFM), quasi-frequency modulation (QFM), sinusoidal amplitude modulation (SAM), and random-phase FM (RPFM). At the lowest modulation frequency (5 Hz) modulation thresholds expressed as AM depth were similar for RPFM, SAM and QFM suggesting the predominance of envelope cues. At the higher modulation frequencies (20 and 40 Hz) thresholds expressed as total frequency excursions were similar for SFM and QFM suggesting a common mechanism, one perhaps based on single-channel FM-to-AM conversion or on a multi-channel place mechanism. The fact that the nominal envelopes of SFM and QFM are different (SFM has a flat envelope), seems to preclude processing based on the envelope of the external stimulus. Also, given the 4-kHz carrier and the similarity to previously published results obtained with a 1-kHz carrier, processing based on temporally-coded fine structure for all four types of modulation appears unlikely.     

Monaural and interaural temporal modulation transfer functions measured with 5-kHz carriers

Temporal modulation transfer functions (TMTFs) were measured for detection of monaural sinusoidal amplitude modulation and dynamically varying interaural level differences for a single set of listeners. For the interaural TMTFs, thresholds are the modulation depths at which listeners can just discriminate interaural envelope-phase differences of 0 and 180 degrees. A 5-kHz pure tone and narrowband noises, 30- and 300-Hz wide centered at 5 kHz, were used as carriers. In the interaural conditions, the noise carriers were either diotic or interaurally uncorrelated. The interaural TMTFs with tonal and diotic noise carriers exhibited a low-pass characteristic but the cutoff frequencies changed nonmonotonically with increasing bandwidth. The interaural TMTFs for the tonal carrier began rolling off approximately a half-octave lower than the tonal monaural TMTF (approximately 80 Hz vs approximately 120 Hz). Monaural TMTFs obtained with noise carriers showed effects attributable to masking of the signal modulation by intrinsic fluctuations of the carrier. In the interaural task with dichotic noise carriers, similar masking due to the interaural carrier fluctuations was observed. Although the mechanisms responsible for differences between the monaural and interaural TMTFs are unknown, the lower binaural TMTF cutoff frequency suggests that binaural processing exhibits greater temporal limitation than monaural processing.     

Effect of modulator asynchrony of sinusoidal and noise modulators on frequency and amplitude modulation detection interference

The effect on modulation detection interference (MDI) of timing of gating of the modulation of target and interferer, with synchronously gated carriers, was investigated in three experiments. In a two-interval, two-alternative forced choice adaptive procedure, listeners had to detect 15 Hz sinusoidal amplitude modulation (AM) or frequency modulation (FM) imposed for 200 ms in the temporal center of a 600 ms target sinusoidal carrier. In the first experiment, 15 Hz sinusoidal FM was imposed in phase on both target and interferer carriers. Thresholds were lower for nonoverlapping than for synchronous modulation of target and interferer, but MDI still occurred for the former. Thresholds were significantly higher when the modulators were gated synchronously than when the interferer modulator was gated on before and off after that of the target. This contrasts with the findings of Oxenham and Dau [J. Acoust. Soc. Am. 110, 402-408 (2001)], who reported no effect of modulation asynchrony on AM detection thresholds, using a narrowband noise modulator. Using FM, experiment 2 showed that for temporally overlapping modulation of target and interferer, modulator asynchrony had no significant effect when the interferer was modulated by a narrowband noise. Experiment 3 showed that, for AM, synchronous gating of modulation of the target and interferer produced lower thresholds than asynchronous gating, especially for sinusoidal modulation of the interferer. Results are discussed in terms of specific cues available for periodic modulation, and differences between perceptual grouping on the basis of common AM and FM.     

Discrimination of modulation depth of sinusoidal amplitude modulation (SAM) noise

The detection of sinusoidal amplitude modulation (SAM) provides a lower bound on the degree to which temporal information in the envelope of complex waveforms is encoded by the auditory system. The extent to which changes in the amount of modulation are discriminable provides additional information on the ability of the auditory system to utilize envelope fluctuations. Results from an experiment on the discrimination of modulation depth of broadband noise are presented. Discrimination thresholds, expressed as differences in modulation power, increase monotonically with the modulation depth of the standard, but do not obey Weber's law. The effects of carrier level and of modulation frequency are consistent with those observed in modulation detection: Changes in carrier level have little effect on modulation discrimination; changes in modulation frequency also have little effect except for standards near the modulation detection threshold. The discrimination of modulation depth is consistent with the leaky-integrator model of modulation detection for standards below--10 dB (20 log ms); for standards greater than--10 dB, the leaky integrator predicts better performance than that observed behaviorally.