Temporal integration and multiple looks, revisited: Weights as a function of time

This study tests the hypothesis that temporal integration for detection of tone bursts with various durations can be explained by optimally combining multiple looks of brief signal segments whose contribution to detection increases over time. Detectability was measured for signals consisting of six consecutive 25-ms, 1-kHz tone pulses presented in a 50-Hz-wide masker or in maskers consisting of seven 50-Hz-wide noises, one critical band apart, with either coherent or incoherent envelopes. The level of each signal pulse varied randomly around masked threshold according to a Gaussian distribution. The slopes of conditional psychometric functions—plotted in terms of $d^{\text{′2}}$ as a function of the squared signal-pulse intensity for pulses in a particular temporal position—yielded estimates of the contribution to detection provided by each pulse. Results for three normal listeners showed a small, but significant, effect of the temporal location of the pulse. Multiple-looks predictions of temporal-integration functions based on the measured weights and on measured psychometric functions were compared to measured temporal-integration functions. For the single-band and incoherent maskers, the predicted temporal-integration slopes were reasonably consistent with those measured, but for the coherent masker it was not. Whereas no current theory can explain the very steep temporal-integration functions obtained in the coherent masker, the present results are not inconsistent with the multiple-looks hypothesis as an explanation for the decrease in threshold with increasing duration of signals presented in random maskers.