Modeling binaural loudness

A survey of data on the perception of binaurally presented sounds indicates that loudness summation across ears is less than perfect; a diotic sound is less than twice as loud as the same sound presented monaurally. The loudness model proposed by Moore et al. [J. Audio Eng. Soc. 45, 224-240 (1997)] determines the loudness of binaural stimuli by a simple summation of loudness across ears. It is described here how the model can be modified so as to give more accurate predictions of the loudness of binaurally presented sounds, including cases where the sounds at the two ears differ in level, frequency or both. The modification is based on the idea that there are inhibitory interactions between the internal representations of the signals at the two ears, such that a signal at the left ear inhibits (reduces) the loudness evoked by a signal at the right ear, and vice versa. The inhibition is assumed to spread across frequency channels. The modified model gives reasonably accurate predictions of a variety of data on the loudness of binaural stimuli, including data obtained using loudness scaling and loudness matching procedures.     

Effects of frequency and duration on psychometric functions for detection of increments and decrements in sinusoids in noise

Psychometric functions for detecting increments or decrements in level of sinusoidal pedestals were measured for increment and decrement durations of 5, 10, 20, 50, 100, and 200 ms and for frequencies of 250, 1000, and 4000 Hz. The sinusoids were presented in background noise intended to mask spectral splatter. A three-interval, three-alternative procedure was used. The results indicated that, for increments, the detectability index d' was approximately proportional to delta I/I. For decrements, d' was approximately proportional to delta L. The slopes of the psychometric functions increased (indicating better performance) with increasing frequency for both increments and decrements. For increments, the slopes increased with increasing increment duration up to 200 ms at 250 and 1000 Hz, but at 4000 Hz they increased only up to 50 ms. For decrements, the slopes increased for durations up to 50 ms, and then remained roughly constant, for all frequencies. For a center frequency of 250 Hz, the slopes of the psychometric functions for increment detection increased with duration more rapidly than predicted by a "multiple-looks" hypothesis, i.e., more rapidly than the square root of duration, for durations up to 50 ms. For center frequencies of 1000 and 4000 Hz, the slopes increased less rapidly than predicted by a multiple-looks hypothesis, for durations greater than about 20 ms. The slopes of the psychometric functions for decrement detection increased with decrement duration at a rate slightly greater than the square root of duration, for durations up to 50 ms, at all three frequencies. For greater durations, the increase in slope was less than proportional to the square root of duration. The results were analyzed using a model incorporating a simulated auditory filter, a compressive nonlinearity, a sliding temporal integrator, and a decision device based on a template mechanism. The model took into account the effects of both the external noise and an assumed internal noise. The model was able to account for the major features of the data for both increment and decrement detection.     

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.     

Factors affecting thresholds for sinusoidal signals in narrow-band maskers with fluctuating envelopes

When a signal is higher in frequency than a narrow-band masker, thresholds are lower when the masker envelope fluctuates than when it is constant. This article investigates the cues used to achieve the lower thresholds, and the factors that influence the amount of threshold reduction. In experiment I the masker was either a sinusoid (constant envelope) or a pair of equal-amplitude sinusoids (fluctuating envelope) centered at the same frequency as the single sinusoid (250, 1000, 3000, or 5275 Hz). The signal frequency was 1.8 times the masker frequency. At all center frequencies, thresholds were lower for the two-tone masker than for the sinusoidal masker, but the effect was smaller at the highest and lowest frequencies. The reduced effect at high frequencies is attributed to the loss of a cue related to phase locking in the auditory nerve. The reduced effect at low frequencies can be partly explained by reduced slopes of the growth-of-masking functions. In experiment II the masker was a sinusoid amplitude modulated at an 8-Hz rate. Masker and signal frequencies were the same as for the first experiment. Randomizing the modulation depth between the two halves of a forced-choice trial had no effect on thresholds, indicating that changes in modulation depth are not used as a cue for signal detection. Thresholds in the modulated masker were higher than would be predicted if they were determined only by the masker level at minima in the envelope, and the threshold reduction produced by modulating the master envelope was less at 250 Hz than at higher frequencies. Experiments III and IV reveal two factors that contribute to the reduced release from masking at low frequencies: The rate of increase of masked threshold with decreasing duration is greater at 250 Hz than at 1000 Hz; the amount of forward masking, relative to simultaneous masking, is greater at 250 Hz than at 1000 Hz. The results are discussed in terms of the relative importance of across-channel cues and within-channel cues.     

Frequency discrimination of complex tones with overlapping and non-overlapping harmonics

These experiments address the following issues. (1) When two complex tones contain different harmonics, do the differences in timbre between them impair the ability to discriminate the pitches of the tones? (2) When two complex tones have only a single component in common, and that component is the most discriminable component in each tone, is the frequency discrimination of the component affected by differences in residue pitch between the two tones? (3) How good is the pitch discrimination of complex tones with no common components when each tone contains multiple harmonics, so as to avoid ambiguity of pitch? (4) Is the pitch discrimination of complex tones with common harmonics impaired by shifting the component frequencies to nonharmonic values? In all experiments, frequency difference limens (DLCs) were measured for multiple-component complex tones, using an adaptive two-interval, two-alternative, forced-choice task. Three highly trained subjects were used. The main conclusions are as follows. (1) When two tones have the first six harmonics in common, DLCs are larger when the upper harmonics are different than when the upper harmonics are in common or are absent. It appears that differences in timbre impair DLCs. (2) Discrimination of the frequency of a single common partial in two complex tones is worse when the two tones have different residue pitches than when they have the same residue pitch. (3) DLCs for complex tones with no common harmonics are generally larger than those for complex tones with common harmonics. For the former, large individual differences occur, probably because subjects are affected differently by differences in timbre. (4) DLCs for harmonic complex tones are smaller than DLCs for complex tones in which the components are mistuned from harmonic values. This can probably be attributed to the less distinct residue pitch of the inharmonic complexes, rather than to reduced discriminability of partials. Overall, the results support the idea that DLCs for complex tones with common harmonics depend on residue pitch comparisons, rather than on comparisons of the pitches of partials.     

The effect of hearing loss on the resolution of partials and fundamental frequency discrimination

The relationship between the ability to hear out partials in complex tones, discrimination of the fundamental frequency (F0) of complex tones, and frequency selectivity was examined for subjects with mild-to-moderate cochlear hearing loss. The ability to hear out partials was measured using a two-interval task. Each interval included a sinusoid followed by a complex tone; one complex contained a partial with the same frequency as the sinusoid, whereas in the other complex that partial was missing. Subjects had to indicate the interval in which the partial was present in the complex. The components in the complex were uniformly spaced on the ERB(N)-number scale. Performance was generally good for the two "edge" partials, but poorer for the inner partials. Performance for the latter improved with increasing spacing. F0 discrimination was measured for a bandpass-filtered complex tone containing low harmonics. The equivalent rectangular bandwidth (ERB) of the auditory filter was estimated using the notched-noise method for center frequencies of 0.5, 1, and 2 kHz. Significant correlations were found between the ability to hear out inner partials, F0 discrimination, and the ERB. The results support the idea that F0 discrimination of tones with low harmonics depends on the ability to resolve the harmonics.     

Dynamic range and asymmetry of the auditory filter

This experiment was designed to measure the shape and asymmetry of the auditory filter over a wider dynamic range than has been measured previously. Thresholds were measured for 2-kHz sinusoidal signals in the presence of two 800-Hz-wide noise bands, one above and one below the signal frequency. The spectrum level of the noise was 45 dB (re: 20 muPa), and the noise bands were placed both symmetrically and asymmetrically about the signal frequency. The deviation of the signal frequency from the nearer edge of each noise band varied from 0 to 0.8 times the signal frequency. Each ear of six subjects was tested, and the subjects' ages ranged from 22 to 74 years. The auditory filters derived from the data were somewhat asymmetric, with steeper slopes on the high-frequency side; the degree of asymmetry varied across subjects. The asymmetry could be characterized as a uniform stretching of the (linear) frequency scale on one side of the filter. The dynamic range of the auditory filter exceeded 60 dB in the younger listeners, but the dynamic range and sharpness of the filter tended to decrease with increasing age.     

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.     

Suggested formulae for calculating auditory-filter bandwidths and excitation patterns

Recent estimates of auditory-filter shape are used to derive a simple formula relating the equivalent rectangular bandwidth (ERB) of the auditory filter to center frequency. The value of the auditory-filter bandwidth continues to decrease as center frequency decreases below 500 Hz. A formula is also given relating ERB-rate to frequency. Finally, a method is described for calculating excitation patterns from filter shapes.     

Frequency discrimination of complex tones; assessing the role of component resolvability and temporal fine structure

Thresholds for discriminating the fundamental frequency (FO) of a complex tone, FODLs, are small when low harmonics are present, but increase when the number of the lowest harmonic, N, is above eight. To assess whether the relatively small FODLs for N in the range 8-10 are based on (partly) resolved harmonics or on temporal fine structure information, FODLs were measured as a function of N for tones with three successive harmonics which were added either in cosine or alternating phase. The center frequency was 2000 Hz, and N was varied by changing the mean FO. A background noise was used to mask combination tones. The value of FO was roved across trials to force subjects to make within-trial comparisons. N was roved by +/- 1 for every stimulus, to prevent subjects from using excitation pattern cues. FODLs were not influenced by component phase for N= 6 or 7, but were smaller for cosine than for alternating phase once N exceeded 7, suggesting that temporal fine structure plays a role in this range. When the center frequency was increased to 5000 Hz, performance was much worse for low N, suggesting that phase locking is important for obtaining low FODLs with resolved harmonics.