A two-filter model for frequency discrimination

Pitch perception at very high frequencies: On psychometric functions and integration of frequency information

Lau et al. [J. Neurosci. 37, 9013-9021 (2017)] showed that discrimination of the fundamental frequency (F0) of complex tones with components in a high-frequency region was better than predicted from the optimal combination of information from the individual harmonics. The predictions depend on the assumption that psychometric functions for frequency discrimination have a slope of 1 at high frequencies. This was tested by measuring psychometric functions for F0 discrimination and frequency discrimination. Difference limens for F0 (F0DLs) and difference limens for frequency for each frequency component were also measured. Complex tones contained harmonics 6-10 and had F0s of 280 or 1400 Hz. Thresholds were measured using 210-ms tones presented diotically in diotic threshold-equalizing noise (TEN), and 1000-ms tones presented diotically in dichotic TEN. The slopes of the psychometric functions were close to 1 for all frequencies and F0s. The ratio of predicted to observed F0DLs was around 1 or smaller for both F0s, i.e., not super-optimal, and was significantly smaller for the low than for the high F0. The results are consistent with the idea that place information alone can convey pitch, but pitch is more salient when phase-locking information is available.

On averaging multiple estimates of decision weights within or across listeners

As a practical guide, a formula is provided for averaging multiple estimates of decision weights, for the purpose of improving the accuracy and reliability of the final estimate of decision weights. The averaging over multiple weight estimates can take place either within or across listeners.

Using individual differences to test the role of temporal and place cues in coding frequency modulation

The question of how frequency is coded in the peripheral auditory system remains unresolved. Previous research has suggested that slow rates of frequency modulation (FM) of a low carrier frequency may be coded via phase-locked temporal information in the auditory nerve, whereas FM at higher rates and/or high carrier frequencies may be coded via a rate-place (tonotopic) code. This hypothesis was tested in a cohort of 100 young normal-hearing listeners by comparing individual sensitivity to slow-rate (1-Hz) and fast-rate (20-Hz) FM at a carrier frequency of 500 Hz with independent measures of phase-locking (using dynamic interaural time difference, ITD, discrimination), level coding (using amplitude modulation, AM, detection), and frequency selectivity (using forward-masking patterns). All FM and AM thresholds were highly correlated with each other. However, no evidence was obtained for stronger correlations between measures thought to reflect phase-locking (e.g., slow-rate FM and ITD sensitivity), or between measures thought to reflect tonotopic coding (fast-rate FM and forward-masking patterns). The results suggest that either psychoacoustic performance in young normal-hearing listeners is not limited by peripheral coding, or that similar peripheral mechanisms limit both high- and low-rate FM coding.

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.

Separating the contributions of primary and unwanted cues in psychophysical studies

A fundamental issue in the design and the interpretation of experimental studies of perception relates to the question of whether the participants in these experiments could perform the perceptual task assigned to them using another feature, or cue, than that intended by the experimenter. An approach frequently used by auditory- and visual-perception researchers to guard against this possibility involves applying random variations to the stimuli across presentations or trials so as to make the "unwanted" cue unreliable for the participants. However, the theoretical basis of this widespread practice is not well developed. In this article, we describe a 2-channel model based on general principles of psychophysical signal detection theory, which can be used to assess the respective contributions of the unwanted cue and of the primary cue to performance or thresholds measured in perceptual discrimination experiments involving stimulus randomization. Example applications of the model to the analysis of results obtained in representative studies from the auditory- and visual-perception literature are provided. In several cases, the results of the model-based analyses indicate that the effectiveness of the randomization procedure was less than originally assumed by the authors of these studies. These findings underscore the importance of quantifying the potential influence of unwanted cues on the results of psychophysical experiments, even when stimulus randomization is used.

Characterizing the dependence of pure-tone frequency difference limens on frequency, duration, and level

This study examined the relationship between the difference limen for frequency (DLF) of pure tones and three commonly explored stimulus parameters of frequency, duration, and sensation level. Data from 12 published studies of pure-tone frequency discrimination (a total of 583 DLF measurements across 77 normal-hearing listeners) were analyzed using hierarchical (or "mixed-effects") generalized linear models. Model parameters were estimated using two approaches (Bayesian and maximum likelihood). A model in which log-transformed DLFs were predicted using a sum of power-law functions plus a random subject- or group-specific term was found to explain a substantial proportion of the variability in the psychophysical data. The results confirmed earlier findings of an inverse-square-root relationship between log-transformed DLFs and duration, and of an inverse relationship between log(DLF) and sensation level. However, they did not confirm earlier suggestions that log(DLF) increases approximately linearly with the square-root of frequency; instead, the relationship between frequency and log(DLF) was best fitted using a power function of frequency with an exponent of about 0.8. These results, and the comprehensive quantitative analysis of pure-tone frequency discrimination on which they are based, provide a new reference for the quantitative evaluation of models of frequency (or pitch) discrimination.

Frequency discrimination under conditions of comodulation masking release (L)

Masked detection thresholds can often be improved by introducing coherent masker amplitude modulation across frequency, a phenomenon referred to as comodulation masking release (CMR). While CMR can be large for detection, it is smaller for supra-threshold tasks, such as intensity discrimination. In this experiment, frequency discrimination for a 1000-Hz tone near threshold was found to be poorer in an amplitude-modulated than a steady bandpass noise. These results parallel previous findings for intensity discrimination. Although this study examined the relatively simple task of frequency discrimination, the results may have implications for more complex tasks, such as speech recognition in fluctuating noise.

Psychometric functions for pure-tone frequency discrimination

The form of the psychometric function (PF) for auditory frequency discrimination is of theoretical interest and practical importance. In this study, PFs for pure-tone frequency discrimination were measured for several standard frequencies (200-8000 Hz) and levels [35-85 dB sound pressure level (SPL)] in normal-hearing listeners. The proportion-correct data were fitted using a cumulative-Gaussian function of the sensitivity index, d', computed as a power transformation of the frequency difference, Δf. The exponent of the power function corresponded to the slope of the PF on log(d')-log(Δf) coordinates. The influence of attentional lapses on PF-slope estimates was investigated. When attentional lapses were not taken into account, the estimated PF slopes on log(d')-log(Δf) coordinates were found to be significantly lower than 1, suggesting a nonlinear relationship between d' and Δf. However, when lapse rate was included as a free parameter in the fits, PF slopes were found not to differ significantly from 1, consistent with a linear relationship between d' and Δf. This was the case across the wide ranges of frequencies and levels tested in this study. Therefore, spectral and temporal models of frequency discrimination must account for a linear relationship between d' and Δf across a wide range of frequencies and levels.

Effects of mindfulness meditation training on anticipatory alpha modulation in primary somatosensory cortex

During selective attention, ∼7-14 Hz alpha rhythms are modulated in early sensory cortices, suggesting a mechanistic role for these dynamics in perception. Here, we investigated whether alpha modulation can be enhanced by "mindfulness" meditation (MM), a program training practitioners in sustained attention to body and breath-related sensations. We hypothesized that participants in the MM group would exhibit enhanced alpha power modulation in a localized representation in the primary somatosensory neocortex in response to a cue, as compared to participants in the control group. Healthy subjects were randomized to 8-weeks of MM training or a control group. Using magnetoencephalographic (MEG) recording of the SI finger representation, we found meditators demonstrated enhanced alpha power modulation in response to a cue. This finding is the first to show enhanced local alpha modulation following sustained attentional training, and implicates this form of enhanced dynamic neural regulation in the behavioral effects of meditative practice.

On the choice of adequate randomization ranges for limiting the use of unwanted cues in same-different, dual-pair, and oddity tasks

A major concern when designing a psychophysical experiment is that participants may use a stimulus feature (cue) other than that intended by the experimenter. One way to avoid this problem is to apply random variations to the corresponding feature across stimulus presentations to make the unwanted cue unreliable. An important question facing experimenters who use this randomization (roving) technique is how large the randomization range should be to ensure that the participants cannot achieve a certain proportion correct by using the unwanted cue, while at the same time avoiding unnecessary interference of the randomization with task performance. Previous researchers have provided formulas for the selection of adequate randomization ranges in yes-no and multiple-alternative forced choice tasks. In this article, we provide figures and tables that can be used to select randomization ranges that are better suited to experiments involving a same-different, dual-pair, or oddity task.

Limiting unwanted cues via random rove applied to the yes-no and multiple-alternative forced choice paradigms

When a random rove is used in a perceptual task to control the influence of an unwanted cue that may confound the decision strategy of primary interest, the effectiveness of the rove is determined by its range. Green [Profile Analysis (Oxford University Press, Oxford, 1988)] provided a formula which allows experimenters to determine the roving range required to ensure that the listeners relying on the unwanted cue cannot exceed a pre-defined percentage of correct responses in a two-interval, two-alternative forced-choice experiment. Here, Green's analysis is extended to the yes-no and m-alternative, forced-choice paradigms (m>2).

On suppressing unwanted cues via randomization

In certain perceptual discrimination tasks, a change in a particular stimulus variable can be perceived as changes along multiple perceptual dimensions. If the study is primarily concerned with a particular perceptual dimension or cue, it is important that the experimenter keep the influences of the other unwanted but correlated perceptual cues under control. One way to accomplish this objective is to randomize the stimuli along the stimulus dimensions primarily associated with these unwanted cues, making them unreliable as a basis for the discrimination. This theoretical note presents a mathematical proof that a uniform randomization is the most effective way of suppressing unwanted cues.

Frequency and intensity discrimination measured in a maximum-likelihood procedure from young and aged normal-hearing subjects

A maximum-likelihood method was applied in measurements of frequency and intensity discrimination for aged and young normal-hearing subjects with closely matched audiograms. This method was preferred over other psychophysical procedures because it is efficient and controls experimental variance, features that are highly desirable for testing aged subjects. In order to implement the method, psychometric functions for each task were also measured from young subjects using a constant-stimuli procedure. For the young subjects, the differential thresholds obtained from these two procedures were generally comparable. Further, both sets of data were consistent with previous literature, indicating that the maximum-likelihood method was successfully applied for frequency and intensity discrimination. A frequency-dependent difference between young and aged subjects in both frequency and intensity discrimination was observed. Even with closely matched audiograms, aged subjects demonstrated poorer discrimination abilities than young subjects. The age-related difference was always largest at 500 Hz and decreased as frequency increased.