Audible Threshold of Early Reflections with Different Orientations and Delays

Early reflection is an important component in an enclosed sound field. Due to the precedence effect, the early reflection may not be the dominant factor in sound source localization; however, it still has obvious influences on spatial position, loudness, timbre, and etc. Till now, there have sparse studies on evaluation of the audible threshold of early reflections with lacking of general and quantitative results. This work investigated the audible threshold of early reflection with a simplified sound field model under various experimental conditions including the combination of eight incidence angles and five time delays. Three-down-one-up adaptive strategy with three-interval three-alternative forced-choice (3I-3AFC) paradigm was used due to its efficiency and robustness. Results indicate that (1) the audible threshold of early reflections decreases monotonically with increasing time delay relative to the direct sound. Furthermore, a linear equation between early reflection threshold and time delay is established with correlation coefficient higher than 0.9; (2) When the direct sound and the reflection locate in the same half-plane, the audible threshold of early reflections decreases with increasing angle deviation between the direct sound and the reflection. Moreover, a front-back symmetry of early reflection threshold is observed for stimuli below 5 kHz; (3) Considerable variations in early reflection threshold are found among individuals, especially at large angle deviation and time delay of early reflections relative to the direct sound.     

The effects of a high-frequency suppressor on tuning curves and derived basilar-membrane response functions

Forward-masked psychophysical tuning curves were obtained using a fixed, low-level signal at a frequency of 4 kHz, and masker frequencies of 2.0, 2.5, 3.0, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, and 5.5 kHz, at masker-signal gaps of 20, 30, 40, 60, 80, and 100 ms. An adaptive two-interval, two alternative forced-choice (21-2AFC) procedure was used to obtain the masker level at threshold. This procedure was repeated with the addition of a 4.75-kHz suppressor at 50 or 60 dB SPL, gated with the masker. Tuning curves were broader, and estimates of compression and gain from derived input/output functions were decreased in the presence of a suppressor as compared to the no-suppressor condition. The results are consistent with physiological results, which show that suppression leads to a broadening of tuning curves and a partial linearization of the midlevel portion of the basilar-membrane input/output function.     

A comparison of adaptive procedures for rapid and reliable threshold assessment and training in naive listeners

In psychoacoustic studies there is often a need to assess performance indices quickly and reliably. The aim of this study was to establish a quick and reliable procedure for evaluating thresholds in backward masking and frequency discrimination tasks. Based on simulations, four procedures likely to produce the best results were selected, and data collected from 20 naive adult listeners on each. Each procedure used one of two adaptive methods (staircase or maximum-likelihood estimation, each targeting the 79% correct point on the psychometric function) and two response paradigms (3-interval, 2-alternative forced-choice AXB or 3-interval; 3-alternative forced-choice oddball). All procedures yielded statistically equivalent threshold estimates in both backward masking and frequency discrimination, with a trend to lower thresholds for oddball procedures in frequency discrimination. Oddball procedures were both more efficient and more reliable (test-retest) in backward masking, but all four procedures were equally efficient and reliable in frequency discrimination. Fitted psychometric functions yielded similar thresholds to averaging over reversals in staircase procedures. Learning was observed across threshold-assessment blocks and experimental sessions. In four additional groups, each of ten listeners, trained on the different procedures, no differences in performance improvement or rate of learning were observed, suggesting that learning is independent of procedure.     

Two-, three-, and four-interval forced-choice staircase procedures: estimator bias and efficiency

Threshold estimates for multiple-interval forced-choice staircase procedures were studied using computer simulations. A sigmoidal psychometric function shape governed the hypothetical subject's responses in the simulations. Parameters varied included the number of trials, the step size for stimulus level change, and decision rules that targeted 70.7% and 79.4% correct performance. Each threshold estimate was calculated by averaging the stimulus levels at which a reversal a stimulus level direction occurred. The results of the simulations suggest that, as the number of alternatives is increased from 2 to 4, the variability of repeated threshold estimates decreases or remains constant, and the accuracy of the estimator, in most cases, improves. A subset of the simulations was compared with data obtained in a detection-in-noise task. The behavioral data were consistent with the simulation results. Two major conclusions were reached. First, 3- and 4-interval forced-choice (IFC) procedures are more efficient than a 2IFC procedure with a decision rule that targets 70.7% correct performance even when the additional time required to complete 3- and 4IFC trials is considered. Second, the accuracy of 2IFC procedures can be improved by fitting the trial history of a staircase run using probit analysis.     

Stimulus selection in adaptive psychophysical procedures

In adaptive psychophysical procedures, the stimulus should be presented at a relatively high level rather than near the middle of the psychometric function, which is often defined as the "threshold" value. For some psychometric functions, the optimal stimulus placement level produces 84% to 94% correct responses in a two-alternative forced-choice task. This result is disquieting because the popular two-down one-up rule tracks a relatively low percentage of correct responses, 70.7%. Computer simulations and a variety of psychometric functions were used to confirm the validity of this analysis. These simulations also demonstrate that the precise form of the psychometric function is not critical in achieving the high efficiencies. Finally, data from human listeners indicate that the standard deviation of threshold estimates is indeed larger when the stimulus presented on each trial is at a stimulus level corresponding to 70.7% rather than 94% correct responses.     

Comparison of Levitt- and Zwislocki-type adaptive procedures for stimulus placement in human listeners

The "3-down, 1-up" adaptive stimulus placement rules attributed to Levitt and Zwislocki were compared in the context of human interaural time difference discrimination, employing otherwise commonly used procedures (e.g., averaging reversals to estimate threshold). The Zwislocki rule typically accumulated over three more reversals than the Levitt rule but the rules were approximately equally efficient. This may be because the additional reversals did not provide additional information or that any additional information was countered by other factors, such as the lower theoretical asymptotic response probability (0.75 vs 0.794). Relative bias between rules was also explored with the aid of a simulation.     

Binocular, Monocular and Dichoptic Pattern Masking

It has been reported that a quadratic summation rule can account for threshold versus masker contrast (TvC) functions for binocular, monocular and dichoptic masking. However, the present study suggests that inputs from two eyes are summed in different ways. Foleys model was revised to describe TvC functions for binocular, monocular and dichoptic masking. The revised model has the following two characteristics. First, the revised model receives two monocular inputs. Secondly, excitations and inhibitory signals are subjected to nonlinear transducer functions before and after summation of the monocular signals. A two-alternative forced-choice procedure was used to measure contrast thresholds for Gaussian windowed sine-wave gratings (target) in the presence of sine-wave gratings (masker). Thresholds were measured for 11 masker contrasts and the three masking conditions. It was shown that this revised model fitted the data resonably well. The revised model indicates how monocular inputs are summed in contrast processing.     

A cautionary note on the use of the adaptive up-down method

Up-down staircases with equal sizes for the steps up and down are widely used to estimate detection and discrimination thresholds in psychoacoustics, but the conventional average-of-reversals estimator does not converge on its presumed percent point in Yes-No tasks or in two-alternative forced-choice detection tasks. The particular percent point of convergence is partly determined by the relative size of the steps with respect to the spread (inverse of slope) of the underlying psychometric function. In particular, threshold is increasingly underestimated as the spread of the psychometric function decreases. This characteristic may have serious consequences when thresholds estimated via up-down staircases are compared across conditions in which the spread of the psychometric function varies, because then these thresholds do not represent comparable measures of performance. This paper documents the misbehavior of the average-of-reversals estimator under up-down rules and types of forced-choice task that are in common use in psychoacoustics but which have not been studied before in simulations. It is also shown that a relatively simple modification of the up-down design (namely, using steps up and down of different size and in a certain ratio depending only on the task and the up-down rule being used) stabilizes the performance of these staircases.     

Forward masking patterns for harmonic complex tones

Complex tones containing the first ten harmonics at equal amplitude, and with fundamental frequencies of 100, 200, or 400 Hz, served as maskers for brief sinusoidal signals (10-, 20-, or 40-ms duration) presented immediately following the maskers. Threshold was measured as a function of signal frequency, using an adaptive, two-alternative forced-choice procedure. The starting phase of the signal relative to the masker had no significant effect on threshold. The masking patterns showed clear peaks corresponding to the first 3 or 4 harmonics, but no peaks were visible for higher harmonics. It is concluded that the "ripple" in the internal spectra of the maskers amounts to 3 dB or less for harmonics above the fifth.     

Level discrimination as a function of level for tones from 0.25 to 16 kHz

Difference limens for level (delta L in dB = 20 log [(p + delta p)/p], where p is pressure) were measured as a function of level for tones at 0.25, 0.5, 1, 2, 4, 8, 10, 12, 14, and 16 kHz. At each frequency, test levels encompassed the range from near threshold to 95 dB SPL in steps of 10 dB or smaller. The stimulus duration was 500 ms and the interstimulus interval was 250 ms. An adaptive two-alternative forced-choice procedure with feedback was used. Results for six normal listeners show individual differences among listeners, but the general trends seen in the average data clearly are present in the individual data and show the following. First, the delta Ls at all but the highest frequencies are generally smaller at high levels than at low levels. Second, the delta Ls at equal SPLs are largely independent of frequency up to about 4 kHz, but increase with frequency above 4 kHz. Third, at 8 and 10 kHz, the delta Ls are clearly nonmonotonic functions of level, showing consistent deterioration in the mid-level delta Ls relative to the low- and high-level delta Ls. The present data are discussed qualitatively in terms of current models of level discrimination.     

Duration discrimination of steady and gliding tones: a new method for estimating sensitivity to rate of change

Thresholds for the detection of differences in duration were measured in a two-alternative, forced-choice task for four types of signals, all centered at 2000 Hz: (1) sinusoids fixed in frequency and level; (2) sinusoids of fixed frequency whose level was swept up or down by 5 or 10 dB; (3) sinusoids of fixed level whose frequency was swept up or down by 100 Hz; and (4) sinusoids whose level was swept up or down by 10 dB and whose frequency was swept up or down by 100 Hz. For types (2)-(4), the direction of the sweeps was fixed within a run. The duration of the standard was either fixed at 750 ms or was varied randomly from trial to trial by up to +/- 7% about 750 ms. The duration of the comparison signal was initially 100 ms greater than that of the standard and was varied adaptively to determine threshold. The pattern of results was similar for all four subjects tested. Duration-discrimination thresholds for the signals that were swept in level and/or frequency were lower than those for the fixed signal, typically by 15-20 ms. This indicates that subjects were sensitive to the rate of change of frequency and/or level and could use this as a cue for duration discrimination. The Weber fraction for rate of change was estimated to be about 0.05-0.06 and was similar for changes in level and in frequency.     

Minimum audible angle thresholds for sources varying in both elevation and azimuth

Minimum audible angle (MAA) thresholds were obtained for four subjects in a two-alternative, forced-choice, three up/one down, adaptive paradigm as a function of the orientation of the array of sources. With sources distributed on the horizontal plane, the mean MAA threshold was 0.97 degrees. With the sources distributed on the vertical plane (array rotated 90 degrees), the mean MAA threshold was 3.65 degrees. Performance in both conditions was well in line with previous experiments of this type. Tests were also conducted with sources distributed on oblique planes. As the array was rotated from 10 degrees-60 degrees from the horizontal plane, relatively little change in the MAA threshold was observed; the mean MAA thresholds ranged from 0.78 degrees to 1.06 degrees. Only when the array was nearly vertical (80 degrees) was there any appreciable loss in spatial resolution; the MAA threshold had increased to 1.8 degrees. The relevance of these results to research on auditory localization under natural listening conditions, especially in the presence of head movements, is also discussed.     

Effects of frequency modulation on absolute, masked, and reflex thresholds

Behavioral and acoustic reflex thresholds were determined for five normal-hearing subjects in response to carrier signals of 500 and 2000 Hz which were unmodulated or modulated sinusoidally at rates of 2, 20, and 200 times per second with frequency deviations (delta f) of 30, 100, and 300 Hz. Behavioral (absolute and masked) thresholds were determined using an adaptive two-alternative forced-choice procedure. Acoustic reflex thresholds were determined by visual inspection of stored reflex waveforms. Frequency modulation was not found to exert a systematic effect at absolute threshold. Frequency modulation did affect threshold estimates systematically, but differentially, at masked threshold and acoustic reflex threshold. Increasing the frequency deviation of the modulation was associated with an increase in masked threshold and with a decrease in acoustic reflex threshold at both test frequencies. The findings are discussed in terms of critical band phenomena.     

The lateralization of simple dichotic pitches

A "simple" dichotic pitch arises when a single narrow band possesses a different interaural configuration from a surrounding broadband noise whose interaural configuration is uniform and correlated. Such pitches were created by interaurally decorrelating a narrow band (experiment 1) or by giving a narrow band a different interaural time difference from the noise (experiment 2). Using an adaptive forced-choice procedure, listeners adjusted the interaural intensity difference of "pointers" to match their lateralization to that of the dichotic pitches. The primary determinants of lateralization were the interaural configuration of the broadband noise (experiment 1), the center frequency of the narrow band (experiment 1), and its interaural configuration (experiment 2). The ability of two computational models to predict these results was evaluated. A version of the central-spectrum model [J. Raatgever and F. A. Bilsen, J. Acoust. Soc. Am. 80, 429-441 (1986)] incorporating realistic frequency selectivity accounted for the main results of experiment 1 but not experiment 2. A new "reconstruction-comparison" model accounted for the main results of both experiments. To accommodate the variables shown to influence lateralization, this model segregates evidence of the dichotic pitch from the noise, reconstructs the cross-correlogram of the noise, and compares it with the cross-correlogram of the original stimulus.     

Control of traveling waves in the Mammalian cortex

We experimentally confirmed predictions that modulation of the neuronal threshold with electrical fields can speed up, slow down, and even block traveling waves in neocortical slices. The predictions are based on a Wilson-Cowan-type integro-differential equation model of propagating neocortical activity. Wave propagation could be modified quickly and reversibly within targeted regions of the network. To the best of our knowledge, this is the first example of direct modulation of the threshold to control wave propagation in a neural system.     

Interaural intensity discrimination: insensitivity at 1000 Hz

Recent data from three laboratories have replicated Mills' [J. Acoust. Soc. Am. 32, 132-134 (1960)] finding that interaural intensity discrimination is relatively poorer for tones of 1000 Hz than for tones of either higher or lower frequencies. To get a finer look at this frequency effect, interaural intensity difference thresholds were obtained from four subjects for tones of several frequencies around 1000 Hz. An adaptive two-interval forced-choice procedure was employed, in which the overall intensity of the signals was varied randomly in order to prevent subjects from listening to monaural loudness changes. Despite large intersubject differences in overall sensitivity to interaural intensity differences, all four subjects showed a local peak in their threshold functions at or near 1000 Hz. This curious "1000-Hz effect" might be explained by imagining that an interaural intensity comparator operates more efficiently as frequency increases, but that a peripheral interaural intensity difference to interaural-time difference conversion contributes to laterality judgments for low-frequency tones, thus acting to lower thresholds again for frequencies below 1000 Hz.     

Integrated photoabsorption strength and sum rules for a bound Dirac particle

Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a few percent. Whereas the total M1-strength is strongly underestimated by the lowest order M1-sum rule, the total E2-strength is reasonably well reproduced up to about 10% by the lowest order E2-sum rule.     

Monaural and binaural auditory frequency resolution measured using bandlimited noise and notched-noise masking

Several studies using bandlimited masking noise have indicated that NOSO frequency resolution is better than that for NOS pi. The present study examined NOSO and NOS pi frequency resolution with two different masking methods: bandlimited noise and notched noise. Noise spectrum levels of 10, 30, and 50 dB/Hz were used. Thresholds were determined for a 500-Hz signal, using a three-alternative forced-choice adaptive procedure, as a function of masker bandwidth and notchwidth. For NOSO presentation, 3-dB down points were comparable for the notched-noise and bandlimiting methods. For NOS pi presentation, 3-dB down points were generally greater for the bandlimiting method than the notched noise method. Furthermore, for NOS pi presentation, the 3-dB down estimate increased as noise level increased for the bandlimiting method, but stayed constant for the notched-noise method. It is suggested that the two masking methods measured different aspects of binaural processing.     

Small-<Emphasis Type="Italic">x</Emphasis> Behavior of Non-singlet Spin Structure Function and Bjorken Sum Rule with pQCD Correction up to NNLO and Higher Twist Correction

A calculation of the non-singlet part of spin dependent structure function, \(xg_{1}^{NS}(x,Q^{2})\) and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with Q ² dependent intercept as the initial input, we have solved the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small-x for \(xg_{1}^{NS}(x,Q^{2})\) and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of \(xg_{1}^{NS}(x,Q^{2})\) and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.     

A comparison of psychophysical procedures for level-discrimination thresholds

Five different psychophysical procedures were used to measure level-discrimination (also called intensity discrimination) thresholds for 1-kHz tones at two levels (30 and 90 dB SPL) and two durations (10 and 500 ms). The procedures were the classic transformed up-down staircase method with a two-alternative forced-choice (2AFC) paradigm (UPD), 15- and 50-trial implementations of the method of maximum likelihood (MML) with a cued yes-no paradigm, and 18-trial implementations of ZEST using both cued yes-no and 2AFC paradigms. Results obtained from nine normal listeners show that estimates of level-discrimination thresholds for the four conditions are similar across all five procedures when different points of convergence are accounted for. The variance of threshold estimates within listener and condition was smallest for UPD, largest for the MML with 15 trials, and statistically indistinguishable among the others. The sweat factors ranged from 5.5 for MML with 50 trials to about 1.4 for UPD and ZEST. Simulations show that ideal performance of procedures may be far from real-life experience and that these deviations are likely to depend on complex interactions between listener behavior and parameter choices used for implementing the procedures. Therefore, empirical verification is important for judging the effectiveness of psychophysical procedures.