Quadratic-compression model of auditory discrimination and detection

Our model of detection and discrimination is based on the common assumption that, for psychoacoustic tasks dominated by a single auditory comparison, d-prime is equal to a perceived-intensity difference divided by the standard deviation of this perceived intensity. In general, the transformation from the external, physical intensity of an acoustic signal to an internal, perceived intensity is nonlinear, compressive, and similar to the transformation from physical intensity to loudness. We represent the compression associated with this intensity transformation by a quadratic function. This leads to explicit mathematical representations of the external-to-internal intensity transformation and its inverse. For psychoacoustic tasks such as intensity discrimination, increment detection, and forward masking, we can write explicit expressions for d-prime and signal threshold. Model predictions based on these expressions are in good agreement with experimental data from the literature, as well as observations from our laboratory. Some of these comparisons between model and data lead to predictions regarding the dependence of internal noise (or variance) on stimulus intensity for intensity discrimination and increment detection. Other comparisons suggest that the influence of neural adaptation on forward masking is greater than the influence of masker persistence. The quadratic-compression model may provide a useful framework for understanding a variety of simple psychoacoustic tasks.