Detection of temporal gaps in sinusoids by normally hearing and hearing-impaired subjects

A two-alternative forced-choice task was used to measure psychometric functions for the detection of temporal gaps in a 1-kHz, 400-ms sinusoidal signal. The signal always started and finished at a positive-going zero crossing, and the gap duration was varied from 0.5 to 6.0 ms in 0.5-ms steps. The signal level was 80 dB SPL, and a spectrally shaped noise was used to mask splatter associated with the abrupt onset and offset of the signal. Two subjects with normal hearing, two subjects with unilateral cochlear hearing loss, and two subjects with bilateral cochlear hearing loss were tested. The impaired ears had confirmed reductions in frequency selectivity at 1 kHz. For the normal ears, the psychometric functions were nonmonotonic, showing minima for gap durations corresponding to integer multiples of the signal period (n ms, where n is a positive integer) and maxima for durations corresponding to (n - 0.5) ms. For the impaired ears, the psychometric functions showed only small (nonsignificant) nonmonotonicities. Performance overall was slightly worse for the impaired than for the normal ears. The main features of the results could be accounted for using a model consisting of a bandpass filter (the auditory filter), a square-law device, and a sliding temporal integrator. Consistent with the data, the model demonstrates that, although a broader auditory filter has a faster transient response, this does not necessarily lead to improved performance in a gap detection task. The model also indicates that gap thresholds do not provide a direct measure of temporal resolution, since they depend at least partly on intensity resolution.     

Mechanisms of modulation gap detection

It has been postulated that the central auditory system contains an array of modulation filters, each responsive to a different range of modulation frequencies present at the outputs of the (peripheral) auditory filters. In the present experiments, we tested what we call the "dip hypothesis," that a gap in modulation is detected using the "dip" in the output of the modulation filter tuned to the modulator frequency. In experiment 1, the task was to detect a gap in the sinusoidal amplitude modulation imposed on a 4-kHz carrier. The modulator preceding the gap ended with a positive-going zero-crossing. There were three conditions, differing in the phase at which the modulator started at the end of the gap; zero-phase, at a positive-going zero-crossing; pi-phase, at a negative-going zero-crossing; and "preserved" phase, at the phase the modulator would have had if it had continued without interruption. Modulation frequencies were 5, 10, 20, and 40 Hz. Psychometric functions for detection of the gap were measured using a two-alternative forced-choice task. For the zero-phase and preserved-phase conditions, the detectability index, d', increased monotonically with increasing gap duration. For the pi-phase condition, performance was good (d' > 1) for small gap durations, and initially worsened with increasing gap duration, before improving again for longer gap durations. This is the pattern of results expected from the dip hypothesis, provided that the modulation filters have Q values of 2 or more. However, it is also possible that a rhythm cue was used to improve performance in the pi-phase condition for short gap durations; the introduction of the gap markedly disrupted the regular rhythm produced by the modulator peaks. In experiment 2, the rhythm cue was disrupted by varying the modulator period randomly around its nominal value, except for the modulator periods immediately before and after the gap. This markedly impaired performance, and resulted in psychometric functions that were very similar for the zero-phase and pi-phase conditions. This pattern of results is inconsistent with the dip hypothesis. For both experiments, modulation gap "thresholds" (d' approximately 1) were roughly constant when expressed as a proportion of the modulator period. Possible mechanisms of modulation gap detection are discussed and evaluated.     

Temporal gaps in noise and sinusoids

The ability of human observers to detect partially filled or completely silent intervals (gaps) was measured using a variety of different waveforms. The slopes of the psychometric functions for gap detection using broadband noise are dependent upon the amount of noise remaining during the gap. For completely silent intervals, the psychometric function covers a range of only 2 ms, but the psychometric functions for partially filled intervals are less steep. The detection of gaps in narrow-band noise (surrounded by complementary band-reject maskers) is strongly influenced by the signal-to-noise ratio. The signal bandwidth and center frequency also influence detectability. Gap detection improved as signal bandwidth increased, and detection improved when signal bands containing gaps were centered at higher frequencies. Detection of gaps in single components of a 21-component, equal-amplitude complex also showed lower thresholds as the frequency of the component containing the gap increased. Increasing the number of components in the complex that contained the gap improved the detectability of the gap, more so when the gaps were all presented at the same time (synchronous condition). Uncertainty about the temporal position of the gap within the observation interval made the gap more difficult to detect. This temporal uncertainty effect occurred for gaps in broadband noise, in narrow-band noise, and in sinusoidal waveforms.     

Detection of temporal gaps in bandlimited noise: effects of variations in bandwidth and signal-to-masker ratio

Thresholds were measured for the detection of a temporal gap in a bandlimited noise signal presented in a continuous wideband masker, using an adaptive forced-choice procedure. In experiment I the ratio of signal spectrum level to masker spectrum level (the SMR) was fixed at 10 dB and gap thresholds were measured as a function of signal bandwidth at three center frequencies: 0.4, 1.0, and 6.5 kHz. Performance improved with increasing bandwidth and increasing center frequency. For a subset of conditions, gap threshold was also measured as bandwidth was varied keeping the upper cutoff frequency of the signal constant. In this case the variation of gap threshold with bandwidth was more gradual, suggesting that subjects detect the gap using primarily the highest frequency region available in the signal. At low center frequencies, however, subjects may have a limited ability to combine information in different frequency regions. In experiment II gap thresholds were measured as a function of SMR for several signal bandwidths at each of three center frequencies: 0.5, 1.0, and 6.5 kHz. Gap thresholds improved with increasing SMR, but the improvement was minimal for SMRs greater than 12-15 dB. The results are used to evaluate the relative importance of factors influencing gap threshold.     

Temporal window shape as a function of frequency and level

In an earlier article [Moore et al., J. Acoust. Soc. Am. 83, 1102-1116 (1988)], preliminary work on the temporal-window model of temporal resolution in the auditory system was described. The temporal window is conceived of as a temporal integrator that slides in time and that is implemented as an intensity-weighting function. The shape of the temporal window was estimated by measuring the threshold for a brief sinusoidal signal presented in a temporal gap between two bursts of noise as a function of the duration of the gap and the position of the signal within the gap. In this paper, a much more thorough examination of the effects of level and frequency on the shape of the window is presented, using the same basic technique. Temporal window shapes were measured at four different frequencies (300, 900, 2700, and 8100 Hz) and at three different masker levels covering a 20-dB range at each frequency. The shape of the temporal window was well described by modeling each side as the sum of two rounded-exponential (roex) functions. The equivalent rectangular duration (ERD) of the window decreased from about 13 to 9 ms as the center frequency increased from 300 to 900 Hz, but decreased only slightly, to 7 ms, as the center frequency increased to 8100. The greater ERD at 300 Hz does not seem to be explicable in terms of "ringing" in the auditory filter. The ERD decreased somewhat with increasing level, for example, having a value of about 10 ms at 2700 Hz with a 20-dB masker spectrum level and about 7 ms with a 40-dB masker spectrum level.     

The shape of the ear's temporal window

This article examines the idea that the temporal resolution of the auditory system can be modeled using a temporal window (an intensity weighting function) analogous to the auditory filter measured in the frequency domain. To estimate the shape of the hypothetical temporal window, threshold was measured for a brief sinusoidal signal presented in a temporal gap between two bursts of noise. The duration of the gap was systematically varied and the signal was placed both symmetrically and asymmetrically within the gap. The data were analyzed by assuming that the temporal window had the form of a simple mathematical expression with a small number of free parameters. The values of the parameters were adjusted to give the best fit to the data. The analysis assumed that, for each condition, the temporal window was centered at the time giving the highest signal-to-masker ratio, and that threshold corresponded to a fixed ratio of signal energy to masker energy at the output of the window. The data were fitted well by modeling each side of the window as the sum of two rounded-exponential functions. The window was highly asymmetric, having a shallower slope for times before the center than for times after. The equivalent rectangular duration (ERD) of the window was typically about 8 ms. The ERD increased slightly when the masker level was decreased, but did not differ significantly for signal frequencies of 500 and 2000 Hz. The temporal-window model successfully accounts for the data from a variety of experiments measuring temporal resolution. However, it fails to predict certain aspects of forward masking and of the detection of amplitude modulation at high rates.     

Temporal integration in the presence of off-frequency maskers

Temporal integration was measured at a relatively low and a relatively high signal frequency under conditions of off-frequency masking. The masker was typically gated for 300 ms, and the signal was presented 70 ms after masker onset. In experiment 1, the signal frequency was 500 or 2000 Hz. Temporal integration was measured in quiet and in the presence of a masker whose frequency was lower or higher than the signal frequency. In all listening situations, there was less integration at 2000 Hz than at 500 Hz. This effect of frequency was particularly dramatic in the presence of a lower frequency masker, where there was almost no integration at 2000 Hz. Experiment 2 showed that this dramatic effect of frequency cannot be understood in terms of the underlying psychometric functions. Experiment 3 measured temporal integration at 750 and 2000 Hz for a large number of masker-signal frequency separations for both a tonal and a noise masker, and in conditions where the masker was gated or continuous. The results with the gated tonal masker largely confirmed the results of experiment 1. The results with the continuous tonal masker and the gated or continuous noise masker, however, were quite different. In those cases, the amount of temporal integration at both signal frequencies was more or less independent of the masker-signal separation; the masked temporal integration was nearly equal to the integration in quiet. Thus based on the conditions evaluated here, off-frequency masked temporal integration differs substantially from integration in quiet only for gated tonal maskers located considerably lower in frequency than the signal. It is unclear how to account for this finding, although it may be related to attentional factors.     

Temporal gap resolution in narrow-band noises with center frequencies from 6000-14000 Hz

Temporal resolution was examined in normal-hearing subjects using a broadband noise and five narrow-band noises with center frequencies (fc) spaced 2 kHz apart between 6 and 14 kHz. Bandwidths of the narrow-band signals were equal to 0.16 fc, and broadband noise maskers with spectral notches were used to restrict the listening bands. Subjects used a Békésy procedure to track the minimum signal level required to keep a periodic temporal gap of fixed duration at threshold. Gap durations from 25 ms to the smallest trackable value were tested with each signal to generate performance curves, which showed the relationship between gap resolution and signal level in the low-to-moderate intensity range. Results showed that gap resolution improved progressively with increased signal level to about 35 dB SL, where minimum gap thresholds of about 3 ms were observed for all signals. These results, when combined with previous low-frequency data, indicate that gap threshold decreases systematically with increased signal frequency to about 5 kHz, and asymptotes at 2-3 ms for higher frequencies. In the context of functional models, the frequency effect is qualitatively consistent with the notion that both the auditory filter and a sensory integrator operate in series to govern temporal resolution in audition.     

Efficient across-frequency integration: evidence from psychometric functions

Across-frequency integration of complex signals was investigated by measuring psychometric functions [log (d') versus signal level in dB SPL] for detection of brief and long signals presented in broadband noise. The signals were tones at 630, 1600, and 4000 Hz, and a nine-tone complex with components spaced at one-third-octave frequencies between 630 and 4000 Hz. The phase relationship of the components in the complex was varied such that adjacent components were in phase (at 0 degrees), 90, or 180 degrees out of phase. Signal durations (defined in terms of the number of cycles between the half-amplitude points of the Gaussian envelopes) of 4.7 and 150 cycles were tested. Results for six normal-hearing listeners showed that the slopes of the psychometric functions were steeper for the brief than for the long signals, and steeper for the tone complexes than for the tones, particularly for the brief signals. This suggests that the transformation from signal intensity to decision variable may be different for brief complex signals than for tonal signals and long complex signals. Thresholds obtained from the psychometric functions were in excellent agreement with those obtained with an adaptive procedure that employed three interleaved tracks. For the long signals, the threshold improvement for the tone complexes relative to a single tone was well described by a 5* log (n) integration rule. However, the threshold improvement for brief signals obeyed a more efficient integration rule of 7 to 8* log (n). A portion of this effect could be accounted for by the phase relationship of the tone complexes; thresholds for brief signals were lowest when the components were in phase at the envelope peak of the signal. This finding indicates that temporal synchrony across auditory channels may enhance detection of brief multi-tone complexes.     

Psychometric functions for gap detection in a yes-no procedure

To examine models of temporal resolution and to investigate the decision processes underlying the detection of a brief pause in a bandpass noise, psychometric functions for gap detection were measured at octave frequencies from 0.25 to 8 kHz. Three normal listeners were tested using a constant-stimulus procedure with a cued Yes-No paradigm. The Minimum Detectable Gap (MDG) estimated from the midpoint of the psychometric functions decreased systematically with increasing frequency. The slopes of the psychometric functions generally increased as the test frequency increased up to 2 kHz, but remained constant at the higher frequencies. Two models were investigated: an energy-detector model and a loudness-detector model. Both consisted of auditory filtering, a nonlinearity, and short-term integration. In the energy-detector model, the nonlinearity was a square law. In the loudness-detector model, it was a compressive power law. Using the usual Gaussian approximations, the energy-detector model fails at low frequencies because the probability distributions of short-term energy differ from Gaussian distributions. The probability distributions of short-term loudness closely follow Gaussian distributions. The loudness-detector model predicts the frequency dependence of the MDG quite accurately, except at 0.25 kHz. It also predicts psychometric functions that resemble the data at low frequencies, but the predicted slopes increase much less with frequency than the measured slopes. This result may indicate that the onset response to the trailing marker of the gap provides an important cue for detection of gaps with durations exceeding the MDG.     

Psychometric functions for gap detection in noise measured from young and aged subjects.

Psychometric functions for gap detection of temporal gaps in wideband noise were measured in a "yes/no" paradigm from normal-hearing young and aged subjects with closely matched audiograms. The effects of noise-burst duration, gap location, and uncertainty of gap location were tested. A typical psychometric function obtained in this study featured a steep slope, which was independent of most experimental conditions as well as age. However, gap thresholds were generally improved with increasing duration of the noise burst for both young and aged subjects. Gap location and uncertainty had no significant effects on the thresholds for the young subjects. For the aged subjects, whenever the gap was sufficiently away from the onset or offset of the noise burst, detectability was robust despite uncertainty about the gap location. Significant differences between young and aged subjects could be observed only when the gap was very close to the signal onset and offset.     

Temporal integration of trains of tone pulses by normal and by cochlearly impaired listeners

Two experiments investigated the temporal integration of trains of tone pulses by normal and by cochlearly impaired listeners. In the first experiment, thresholds were measured for a single 5-ms, 4-kHz tone pulse, and for ten such tone pulses as a function of interpulse interval (delta t). For normal listeners, temporal integration, defined as the threshold difference between one and ten pulses, was about 8 dB for delta t less than 20 ms, and about 5 dB at longer delta t's. For impaired listeners, temporal integration was only about 2-3 dB across the range of delta t's (5-160 ms) studied. A second experiment measured psychometric functions (log d' versus log signal power) for a single pulse and for ten pulses with delta t's of 5 ms and 80 ms. The normal listeners' functions had slopes close to unity in all three conditions, with a few exceptions. The impaired listeners' functions had slopes close to unity for ten pulses with delta t = 5 ms, but had slopes significantly greater than unity for delta t = 80 ms, and for a single pulse. At delta t = 80 ms, the increase in d' relative to the condition with a single tone was similar (a factor of square root of 10) for both impaired and normal listeners, but the threshold difference was smaller for the impaired listeners due to their steeper psychometric functions. For impaired listeners, then, temporal integration at delta t = 80 ms was normal in terms of a change in d' but abnormal when measured as a threshold difference.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effects of non-simultaneous masking on the binaural masking level difference

The present study sought to clarify the role of non-simultaneous masking in the binaural masking level difference for maskers that fluctuate in level. In the first experiment the signal was a brief 500-Hz tone, and the masker was a bandpass noise (100-2000 Hz), with the initial and final 200-ms bursts presented at 40-dB spectrum level and the inter-burst gap presented at 20-dB spectrum level. Temporal windows were fitted to thresholds measured for a range of gap durations and signal positions within the gap. In the second experiment, individual differences in out of phase (NoSπ) thresholds were compared for a brief signal in a gapped bandpass masker, a brief signal in a steady bandpass masker, and a long signal in a narrowband (50-Hz-wide) noise masker. The third experiment measured brief tone detection thresholds in forward, simultaneous, and backward masking conditions for a 50- and for a 1900-Hz-wide noise masker centered on the 500-Hz signal frequency. Results are consistent with comparable temporal resolution in the in phase (NoSo) and NoSπ conditions and no effect of temporal resolution on individual observers' ability to utilize binaural cues in narrowband noise. The large masking release observed for a narrowband noise masker may be due to binaural masking release from non-simultaneous, informational masking.     

The detection of temporal gaps as a function of frequency region and absolute noise bandwidth.

Temporal gap detection was measured as a function of absolute signal bandwidth at a low-, a mid-, and a high-frequency region in six listeners with normal hearing sensitivity. Gap detection threshold decreased monotonically with increasing stimulus bandwidth at each of the three frequency regions. Given conditions of equivalent absolute bandwidth, gap detection thresholds were not significantly different for upper cutoff frequencies ranging from 600 to 4400 Hz. A second experiment investigated gap detection thresholds at two pressure-spectrum levels, conditions typically resulting in substantially different estimates of frequency selectivity. Estimates of frequency selectivity were collected at the two levels using a notched-noise masker technique. The gap threshold-signal bandwidth functions were almost identical at pressure-spectrum levels of 70 dB and 40 dB for the two subjects in experiment II, while estimates of frequency selectivity showed poorer frequency selectivity at the 70-dB level than at 40 dB. Data from both experiments indicated that gap detection in bandlimited noise was inversely related to signal bandwidth and that gap detection did not vary significantly with changes in signal frequency over the range of 600 to 4400 Hz. Over the range of frequencies investigated, the results indicated no clear relation between gap detection for noise stimuli and peripheral auditory filtering.     

Spectral integration and wideband analysis in gap detection and overshoot paradigms

Several listening conditions show that energy remote from a target frequency can deleteriously affect sensitivity. One interpretation of such results entails a wideband analysis involving a wide predetection filter. The present study tested the hypothesis that both temporal gap detection and overshoot results are consistent with a wideband analysis, as contrasted with statistical combination of information across independent channels. For gap detection, stimuli were random or comodulated 50-Hz-wide noise bands centered on 1000, 1932, 3569, and 6437 Hz. For overshoot, the masker was an 8-kHz low-pass filtered noise, with 5-ms tone bursts presented at the same center frequencies used for gap detection. Signals were presented with either 0- or 250-ms delay after masker onset. In each paradigm, the target was introduced at only one frequency or at all four frequencies. Results from gap detection conditions did not favor a wideband analysis interpretation: Results in the random condition were consistent with an optimal combination of cues across frequency. An across-channel interference effect was also evident when only one of the four bands contained the gap. Although results from the overshoot conditions were consistent with a wideband analysis interpretation, they were more parsimoniously accounted for in terms of statistical combination of information.     

The temporal course of masking and the auditory filter shape

Recent experiments have shown that frequency selectivity measured in tone-on-tone simultaneous masking improves with increasing delay of a brief signal relative to the onset of a longer duration gated masker. To determine whether a similar improvement occurs for a notched-noise masker, threshold was measured for a 20-ms signal presented at the beginning, the temporal center, or the end of the 400-ms masker (simultaneous masking), or immediately following the masker (forward masking). The notch width was varied systematically and the notch was placed both symmetrically and asymmetrically about the 1-kHz signal frequency. Growth-of-masking functions were determined for each temporal condition, for a noise masker without a spectral notch. These functions were used to express the thresholds from the notched-noise experiment in terms of the level of a flat-spectrum noise which would produce the same threshold. In simultaneous masking the auditory filter shapes derived from the transformed data did not change significantly with signal delay, suggesting that the selectivity of the auditory filter does not develop over time. In forward masking the auditory filter shapes were sharper than those for simultaneous masking, particularly on the high-frequency side, which was attributed to suppression.     

Estimating the transition bandwidth between two auditory processes: evidence for broadband auditory filters

A spectral discrimination task was used to estimate the frequency range over which information about the temporal envelope is consolidated. The standard consisted of n equal intensity, random phase sinusoids, symmetrically placed around a signal component. The signal was an intensity increment of the central sinusoid, which on average was 1000 Hz. Pitch cues were degraded by randomly selecting the center frequency of the complex and single channel energy cues were degraded with a roving-level procedure. Stimulus bandwidth was controlled by varying the number of tones and the frequency separation between tones. For a fixed frequency separation, thresholds increased as n increased until a certain bandwidth was reached, beyond which thresholds decreased. This discontinuity in threshold functions suggests that different auditory processes predominate at different bandwidths, presumably an envelope analysis at bandwidths less than the breakpoint and across channel level comparisons for wider stimulus bandwidths. Estimates of the "transition bandwidth" for 46 listeners ranged from 100 to 1250 Hz. The results are consistent with a peripheral filtering system having multiple filterbanks.     

Tonal masking and frequency selectivity for the monaural and binaural hearing systems

A series of masking experiments was performed with the aim of comparing frequency selectivity for the monaural and binaural systems. The masking stimulus used in this study combined a sinusoid, which was gated simultaneously with the signal, with a continuous broadband noise. Signal frequency was fixed at 500 Hz. In one condition, the tonal masker and noise were interaurally in phase and the signal was phase reversed. In a second condition, noise, tonal masker, and signal were presented to one ear alone. Signal thresholds were obtained as a function of masker frequency for these two conditions. After making an appropriate selection of noise levels, masking functions for the monaural and binaural system conditions were found to agree closely except for a region about their tips where the binaural condition was more detectable. Two possible interpretations of these results are discussed. Either the monaural and binaural systems contain filters each which have similarly shaped skirts, or the frequency selectivity observed under both diotic and dichotic conditions (for large frequency separations of masker and signal) reflect the operation of a common peripheral filter.     

Spectral differences in the ability of temporal gaps to reset the mechanisms underlying overshoot

When very brief tonal signals are presented immediately after the onset of a gated noise masker, detectability can be 10-20 dB worse than when the signal is delayed by several hundred milliseconds, an effect known as the overshoot. It has long been known that, when an "onset" is created in an otherwise continuous, broadband masker by briefly turning it off and on again, the detectability of a brief signal presented soon after this temporal gap will decline gradually as the gap is increased from a few milliseconds to a few hundred milliseconds. In other words, the auditory system recovers to its quiescent, resting state following an adequate silent interval. Here, the broadband maskers consisted of three adjacent spectral bands--one centered on the frequency of the tonal signal, one low passed below the lower edge of the center band, and one high passed above the upper edge of the center band. The signal was a 2500-Hz tone having a total duration of 6 ms. In different blocks of trials, either all three bands, only the center band, or only the two flanking bands were temporally gapped by a duration ranging from 10-300 ms. When the center band was about 750 Hz wide (about 2.5 critical bandwidths), this differential gapping process resulted in typical recovery functions when all three bands (the entire spectrum) or when just the two flanking bands were gapped. However, when only the center band was gapped, there was no evident recovery--rather, detectability remained near the signal level required with a continuous masker, even for a gap duration of 300 ms.(ABSTRACT TRUNCATED AT 250 WORDS)     

Gap detection and masking in hearing-impaired and normal-hearing subjects

Subjects with cochlear impairments often show reduced temporal resolution as measured in gap-detection tasks. The primary goals of these experiments were: to assess the extent to which the enlarged gap thresholds can be explained by elevations in absolute threshold; and to determine whether the large gap thresholds can be explained by the same processes that lead to a slower-than-normal recovery from forward masking. In experiment I gap thresholds were measured for nine unilaterally and eight bilaterally impaired subjects, using bandlimited noise stimuli centered at 0.5, 1.0, and 2.0 kHz. Gap thresholds were usually larger for the impaired ears, even when the comparisons were made at equal sensation levels (SLs). Gap thresholds tended to increase with increasing absolute threshold, but the scatter of gap thresholds was large for a given degree of hearing loss. In experiment II threshold was measured as a function of the delay between the onset of a 210-ms masker and the onset of a 10-ms signal in both simultaneous- and forward-masking conditions. The signal frequency was equal to the center frequency of the bandlimited noise masker, which was 0.5, 1.0, or 2.0 kHz. Five subjects with unilateral cochlear impairments, two subjects with bilateral impairments, and two normal subjects were tested. The rate of recovery from forward masking, particularly the initial rate, was usually slower for the impaired ears, even when the maskers were presented at equal SLs. Large gap thresholds tended to be associated with slow rates of recovery from forward masking.