Search

This is a brief report on the use of maximum-likelihood (ML) estimators in auditory psychophysics. Slope parameters of psychometric functions are characterized for three nonintensive auditory tasks: forced-choice discrimination of interaural time differences (delta ITD), frequency (delta f), and duration (delta t). Using these slope estimates, the ML method is implemented and threshold estimates are obtained for the three tasks and compared with previously published data. delta ITD thresholds were additionally measured for human observers by means of two other psychophysical procedures: the constant-stimuli (CS) and the 2-down 1-up methods (Wetherill & Levitt, 1965). Standard errors were smallest for the ML method. Finally, simulations showed ML estimates to be more efficient than the CS and k-down 1-up procedures for k = 2 to 5. For up-down procedures, efficiency was highest for k values of 3 and 4. The entropy (Shannon, 1949) of ML estimates was the smallest of the simulated procedures, but poorer than ideal by 0.5 bits.

A correlation technique was used to assess the decision rules of three listeners in two cases of spectral-shape discrimination tasks. In one case the signal frequency was fixed, and in the other it was randomly varied within each block of trials. In order to estimate the decision rule of the listeners, the experimenter superimposed random level perturbations on each frequency component upon each stimulus presentation. Over many trials, correlation coefficients were computed between the random perturbations and the binary responses of the listeners, and were expressed as a function of signal level. For both the fixed- and random-signal cases, the measured correlation functions were in reasonably good agreement with those predicted based on the likelihood-ratio decision rules. Thus the listeners appeared to use information nearly optimally in discriminating spectral shapes. This investigation demonstrated that the correlation technique can be used to reveal the decision rules for cases where the decision statistics are nonlinear functions of the observations.

An adaptive, maximum likelihood (ML) procedure was assessed as an automated tool for estimating audiometric pure-tone thresholds in the clinic under computer control. Pure-tone air-conduction thresholds were measured from 101 workmen who received annual hearing rechecks as part of their employee hearing conservation program. A pure-tone threshold was measured bilaterally for each of the standard audiometric frequencies in a 15-trial block to yield 60 percent correct detection with the ML procedure. The workmen were tested on a modified "yes-no" task. On a trial, the signal was presented in a visually cued 200-msec observation interval. Each workman then had 1000 msec to make a "yes" response. If the workman did not respond during the 1000-msec response period, then the computer assumed a "no" response. After either the "yes" or "no" response, the computer adjusted the signal level for the next trial. The thresholds measured by ML procedure compared favorably with thresholds measured from the same listeners by conventional (CONV) audiometry. The efficiency of the ML procedure was also compared in terms of the time necessary for an experienced audiologist to instruct the listener and perform CONV audiometry. CONV audiometry (3-4 minutes per listener) required about half of the time needed for the ML procedure (6-7 minutes per listener). The relatively longer time associated with measuring an audiogram with the ML procedure was due primarily to more trials being used to estimate threshold.

The ability of listeners to detect the temporal asynchrony of a single harmonic in complex sounds was measured. The listeners discriminated an asynchronous complex from one in which all harmonics were synchronous (standard). The asynchrony was created either at the onset or offset of the complex. In the asynchronous complex, one component either began or ended after all other components in the complex, or it began or ended prior to all other components in the complex. The phase of the signal component was systematically varied in the range from 0 degrees to 180 degrees. All nonsignal components had the same sine phase. The results show that detecting the asynchrony at the onset is superior when all components are in sine phase. Altering the phase of the signal component increased thresholds by as much as a factor of 50, with the largest thresholds obtained when the signal component was inverted in phase. For offset conditions, the phase of the signal component had a much smaller and less consistent effect. Some of the observed effects of phase on the asynchrony thresholds can be understood by considering the response of the Roex filter [Patterson et al., J. Acoust. Soc. Am. 72, 1788-1803 (1982)] centered at the signal frequency.

Standing waves, in the ear canal are created by the interference of two plane waves of the same frequency traveling in opposite directions. One manifestation of this phenomena is that any lateral motion of the transducer produces a change in the length of the canal and therefore, in general, a change in the sound level at the eardrum. Because of the smaller wavelength at the higher frequencies, the changes produced by movement of the transducer will be larger for the higher frequencies than for the lower frequencies. Thus, when the transducer is removed and replaced between successive threshold estimates, it is expected, from physical principles alone, that the intrasubject reliability of the estimates should be better at the lower frequencies. Previous studies, however, have shown that the intrasubject reliability of threshold estimates is nearly the same at both the low (0-8 kHz) and the high (8-16 kHz) frequency regions. A possible explanation for these anomalous results is proposed. While it is found that transducer placement increases the variability of threshold estimates more at the higher frequencies, it has also been found that conventional headphones reduce the size of the standing wave ratios compared with a hard wall termination. An additional factor is the steeper slope of the psychometric function at the higher frequencies. The combination of these factors produces a standard deviation for threshold estimates that is only about 1 dB larger at the high than at the low frequency region.

The ability to detect a mistuned component in a harmonic complex was measured as a function of harmonic number under three different stimulus procedures: simultaneous monotic, successive monotic, and simultaneous dichotic. In the first experiment, the fundamental frequency was 200 Hz, and the stimulus duration was 410 ms. The threshold obtained in the simultaneous-monotic procedure was lower than those obtained in the other two procedures, especially for harmonics above the third. It is argued that an envelope cue associated with lower-frequency components in the power spectrum of the envelope was the primary cue for the detection of a mistuned component in a harmonic complex in the simultaneous-monotic procedure. Thresholds did not differ for successive-monotic and simultaneous-dichotic procedures, suggesting that the detection of the mistuning was mediated above the level of the cochlea. In the second and third experiments, the stimulus duration and the fundamental frequency of the complex was altered. The envelope cue seemed to be weakened by decreasing the stimulus duration and by increasing the fundamental frequency.

Spectral shape discrimination for harmonic complexes with 100-, 200-, or 400-Hz fundamental was investigated in two sets of experiments. In the first set, the signal was an increment in a single component of an otherwise equal-amplitude complex. The results of these experiments showed nearly a 30-dB increase in thresholds as the signal frequencies increased from 1000 to 5000 Hz. A transformation of data based on the assumption that the critical detection quantity is the change in the level in a critical band centered at the signal frequency was applied to remove the effects of the nonsignal components. The corrected thresholds have a bowl-like shape similar to that seen in studies of spectral shape discrimination of stimuli with components equally spaced on a logarithmic frequency scale. Additional experiments examined the effects of the number of components in the complex and the relative phase of the components of the harmonic complex. In the second set of experiments, the effects of local masking were examined either by increasing the level of several adjacent components, or by removing nonsignal components near a single signal component. Again, the results with harmonic signals are similar to those obtained with components spaced at equal intervals on a logarithmic frequency scale, if one calculates the increment in the level produced in a critical band centered at the signal frequency.

The ability of listeners to detect asynchrony in either the temporal onset or offset of individual components in a multicomponent complex was investigated. A standard stimulus was created having a simple kind of asynchrony by linearly delaying successive components of a complex stimulus. Additional asynchrony (the signal) was created by altering the temporal position of a single component of the complex relative to its temporal position in the standard. Asynchrony discrimination was measured for harmonic signals (experiment I) and for complexes in which the components were logarithmically spaced in frequency (experiment II). For the onset condition, asynchrony in either the harmonic or logarithmic complex greatly increased the difficulty in detecting the temporal asynchrony of a single component. For the offset condition, asynchrony discrimination was not greatly affected by asynchrony in the standard.

The ability of listeners to detect asynchrony in either the temporal onset or offset of components in multicomponent complexes was measured. The listener discriminated a standard complex, one in which all components were synchronous, from an asynchronous complex. In the initial experiments, asynchrony was created by starting (onset experiments) or ending (offset experiments) the harmonics at times drawn from a Gaussian distribution. In later experiments, asynchrony was created by starting or terminating only certain components before or after the other components in the complex. One complex consisted of 20 harmonic components with a fundamental of 200 Hz. Another multicomponent complex used components spaced at equal intervals in logarithmic frequency (200 to 4000 Hz). The parameters investigated were rise or decay time of components, duration of a complex, and frequency position of displaced components. The obtained thresholds were different for onset and offset asynchrony. For onset asynchrony in harmonic complexes, the thresholds were a nonmonotonic function of rise time with a minimum of 0.2 ms obtained for a rise time of 1 ms. For offset asynchrony, thresholds were generally monotonic with increases in decay time and ranged from 0.45-1.3 ms. Experiments with a much shorter signal duration demonstrated that forward and backward masking played little role in the observed differences in thresholds. Onset thresholds for harmonic stimuli measured as a function of the frequency region of the asynchronous component(s) showed a minimum of 0.2 ms at about 2000 Hz. The thresholds for offset were about ten times larger. For logarithmic complexes, in some conditions, thresholds were larger by nearly two orders of magnitude. Experiments in which the listeners discriminated changes either in the onset or offset envelope of the wideband stimulus suggest that detection of temporal asynchrony depends on comparison between frequency channels rather than on differences in the temporal onset or offset of the overall energy of the sounds.

Measurements are reported on the detectability of signals added to narrow-band sounds. The narrow-band sounds had a bandwidth of 20 Hz and were either Gaussian noise with flat amplitude spectra or sets of equal-amplitude sinusoidal components whose phases were chosen at random. Four different kinds of sinusoidal signals were used. Two signals produced symmetric changes in the audio spectrum adding a component either at the center of the spectrum or at both ends. The other two signals produced asymmetric changes adding a component at either end of the spectrum. The overall level of the sound was randomly varied on each presentation, so that the presence of a signal was largely unrelated to the absolute level of the signal component(s). A model is proposed that assumes the detection of the symmetric signals is based on changes in the shape of the power spectrum of the envelope. Such changes in the envelope power spectrum are probably heard as changes in the "roughness" or "smoothness" of the narrow-band sound. The predictions of this model were obtained from computer simulations. For the asymmetric signals, the most probable detection cues were changes in the pitch of the narrow-band sound. Results from a variety of different experiments using three listeners support these conjectures.

Interaural envelope delays were measured in six human subjects as a function of the location of a movable sound source, bandpassed between 3 and 16 kHz. A total of 324 source locations were tested in horizontal and vertical increments of 10 degrees. A method is described for estimating the complex directional transfer function of the external ear, independent of the position of the recording microphone in the ear canal. To compute interaural envelope delays, directional transfer functions from the left and right ears were convolved with a critical-band filter, the envelopes were computed, and the envelopes were cross correlated. Interaural envelope delays, as well as interaural group delays, varied somewhat with the center frequency of the critical-band filter and with the vertical location of the sound source. Nevertheless, to a first approximation, envelope delays measured in the ear canals increased monotonically with increasing angle of incidence relative to the median plane, as they would for two microphones on the surface of a rigid sphere. The results are discussed in relation to the possible contribution of interaural envelope delays to sound localization behavior.

Measurements are reported on the ability of observers to discriminate whether the envelope of two amplitude-modulated sinusoids are in phase or out of phase. Spacing between the two carriers was either 2/3 or 4/3 octave, and the depth of modulation was varied to determine threshold. Discrimination performance improved as the level of the carriers increases up to about 60 dB SPL. The frequency locus of the two carriers (geometric mean of the two frequencies), which varied from 500 to 8000 Hz in different experiments, had little effect on discrimination accuracy. Discrimination performance was relatively constant for modulation rates below 100 Hz and deteriorates for higher modulation rates. These results are compared with data obtained from comodulation masking release experiments.

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.

Masking of low-frequency sinusoids of varying durations by Gaussian noise of varying spectral shape was measured in three different studies. Common solutions to technical problems associated with control and specification of low-frequency signals were used in the three studies. If interpreted in terms of Fletcher's critical ratio assumptions, data from the first study lead to the inference that the masking bandwidth is inversely related to signal frequency below about 200 Hz. Data from the second study rule out the likelihood that the apparent increase in masking bandwidth is attributable to changes in auditory integration times at low frequencies. The data of the third study suggest that the apparent increase in auditory filter bandwidth at low frequencies is more adequately explained by a decrease in observers' detection efficiency than by broadening of the filter bandpass.

Temporal acuity, the minimum time interval within which the auditory system can discriminate the order of auditory events, was measured for three listeners with normal hearing and for 10 listeners with sensorineural hearing loss. Eight of the 10 listeners with sensorineural loss showed better temporal acuity for conditions with greater loss. The remaining two listeners showed the opposite effect. The temporal acuity results are not well correlated with either speech discrimination scores or measures of recruitment. The temporal acuity results do appear to be correlated with results observed in studies of temporal integration or brief-tone audiometry. Listeners with sensorineural loss tend to have both poor temporal integration and good temporal acuity. This suggests that the two temporal measures may reflect a single time constant in the auditory system.

The effects of signal uncertainty on detection performance were measured using a new procedure that allows precise specification of the initial temporal uncertainty. Five different models of the detection process, two assuming a continous representation of the sensory input and three assuming a discrete representation, were compared with the obtained data. The effects of varying signal uncertainty (the number of potential signal intervals was one, five, or ten) had little effect on detection performance. The one-parameter form of the choice model can be rejected without hesitation. The continuous Gaussian model and the symmetric two-state model are significantly different from the data. The high threshold and sophisticated two-state models provide accurate descriptions of the data that cannot be rejected on statistical grounds.

Changes in sound pressures measured in the ear canal are reported for broadband sound sources positioned at various locations about the subject. These location-dependent pressures are one source of acoustical cues for sound localization by human listeners. Sound source locations were tested with horizontal and vertical resolution of 10 degrees. Sound levels were measured with miniature microphones placed inside the two ear canals. Although the measured amplitude spectra varied with the position of the microphone in the ear canal, it is shown that the directional sensitivity at any particular frequency of the broadband stimulus is independent of microphone position anywhere within the ear canal. At any given frequency, the distribution of sound pressures as a function of sound source location formed a characteristic spatial pattern comprising one or two discrete areas from which sound sources produced maximum levels in the ear canal. The locations of these discrete areas varied in horizontal and vertical location according to sound frequency. For example, around 8 kHz, two areas of maximum sensitivity typically were found that were located laterally and were separated from each other vertically, whereas, around 12 kHz, two such areas were found located on the horizontal plane and separated horizontally. The spatial patterns of sound levels were remarkably similar among different subjects, although some frequency scaling was required to accommodate for differences in the subjects' physical sizes. Interaural differences in sound-pressure level (ILDs) at frequencies below about 8 kHz tended to increase monotonically with increasing distance of the sound source from the frontal midline and tended to be relatively constant as a function of vertical source location. At higher frequencies, however, ILDs varied both with the horizontal and with the vertical location of the sound source. At some frequencies, asymmetries between the left and right ears in a given subject resulted in substantial ILDs even for midline sound sources. These results indicate the types of horizontal and vertical spatial information that are available from sound level cues over various ranges of frequency and, within a small subject population, indicate the nature of intersubject variability.

A multiple regression analysis of sequential effects in magnitude estimation and absolute identification is presented as an alternative to the approach used by Lockhead and his students. The new analysis indicates that sequential effects do not extend over more than one trial. This is in agreement with the response ratio hypothesis. A more detailed multiple regression analysis of these sequential effects indicates that the magnitude of the correlation between successive responses is heavily dependent on the decibel difference between successive signals. This is not in agreement with the response ratio hypothesis, and the hypothesis is reformulated to take account of this finding. This modification of the model is tested by comparing distributions of normalized responses to theoretical distributions suggested by the model and to a possible alternative distribution.

In most of the previous studies (see Green, 1987) concerning the detection of a change in spectral shape, or "profile analysis," the listener's task was to detect an increment to a single component of an otherwise equal-amplitude, multicomponent background. An important theoretical issue is whether listeners' sensitivity to more complex spectral changes can be predicted from these results. In the present investigation, the sensitivity of a single group of listeners to a wide variety of simple and complex spectral changes was determined. After collecting the data, it was noted that almost all the thresholds could be predicted by a simple calculation scheme that assumed detection of a change in spectral shape occurs when the addition of the signal to the flat, multicomponent background produces a sufficient difference in level between only two regions of the spectrum. Unfortunately, this scheme, while successful for our limited set of data, fails to account for other "profile" data, namely, those obtained when the number of components is altered.

This paper explores how amplitude modulation influences the detection of changes in spectral shape. We generally used a complex of 21 equal-amplitude components, the lowest frequency was 200 Hz, the highest 5000 Hz, with equal logarithmic spacing between components. The signal was an increase in level of one or more components of the complex. The overall level of the sound varied randomly over a 20-dB range. Three experiments are reported. In the first, we determined how the modulation of a single-frequency component influenced the detection of amplitude change at that region. In the second experiment, the signal was an alteration of the entire spectrum and that alteration was subjected to various forms of amplitude modulation. In neither experiment did modulation generally increase the detectability of the signal. Finally, in the third experiment, we determined the effects of modulating the 'signal' and 'nonsignal' parts of the spectrum in different relative phases. The results of this experiment showed that the relative phase is important only for modulation rates slower than about 40 Hz. For faster rates, the temporal structure of the spectrum is unimportant. Thus, for modulation rates above 40 Hz, only the power spectrum of the stimulus is critical.