Modelling detection thresholds for sounds repeated at different delays

Detection thresholds for pairs or multiple copies of sounds are better than those for a single sound, an observation commonly interpreted as indicating temporal integration by the auditory system. Detection thresholds for pairs of brief tones depend on the delay between the tones (if short) and on frequency, suggesting frequency-dependent temporal overlap of auditory-filter responses elicited by the two successive stimuli (Krumbholz and Wiegrebe, 1998). The model presented by Krumbholz and Wiegrebe did not account for all aspects of their data, despite its complexity. This study shows that a simple probabilistic model based on Neubauer and Heil (2008) predicts the increase in threshold for short temporal delays as well as the asymptotic behaviour towards longer delays. The model entails (i) a 4th-order gammatone filter with a brief impulse response and thus broad bandwidth (shorter and broader than those of a filter normally assumed), (ii) the formation of stochastic 'spikes' or 'events' whose probability of occurrence is proportional to the filter output (half-wave rectified fine-structure or amplitude envelope), raised to a power of 3, and (iii) probability summation. The same model with the same front-end filter also predicts thresholds for pairs of clicks presented in band-reject noise, measured by Hall and Lummis (1973). The model accurately predicts the magnitudes and the decay of the alternating increase and decrease of thresholds as the delay between the click varies, the small effects of click polarity, and the dependence of thresholds for pairs of clicks with unequal intensities on their temporal order. Finally, we show that this model also correctly predicts the decrease in threshold with increasing number of temporally separated brief sounds, reported in several studies. While the latter data do not constrain the characteristics of the front-end filter, they do confirm the exponent of 3 in the model. Our paper stresses the viability of the model and raises the possibility that the bandwidths of filters estimated with psychophysical techniques may depend more strongly on the experimental paradigms and stimuli than hitherto thought.