Modeling the additivity of nonsimultaneous masking

Thresholds were measured for detecting a brief 6-kHz sinusoidal signal preceded by a broadband noise masker (forward masking), followed by the masker (backward masking), or both preceded by and followed by the masker (combined masking). The masker-signal interval was systematically varied. Consistent with the literature, thresholds in the combined-masking condition were higher than would be predicted by an energy-sum of the effects of the individual forward and backward maskers. This is often referred to as 'excess' masking. The data were modeled by subjecting the amplitude of the stimuli to a power-law nonlinearity followed by a sliding temporal integrator ('window'). It was assumed that threshold corresponds to a fixed signal-to-noise ratio at the output of the window. The best fits to the data were obtained using a power less than unity (0.5 to 0.7), i.e. by a compressive nonlinearity. Generally good fits to the data were achieved, indicating that the model is able to account for the decay of forward and backward masking as well as the effects of combining pairs of maskers (excess masking). The temporal windows derived from the data are also able to predict thresholds in decrement and increment detection tasks, and to account for the longer-term effects of masker duration in forward masking.