Nonlinearities in the coding of intensity within the context of a temporal summation model

A model of temporal summation and intensity coding relates the subject's internal percept y(t) to the stimulus input x(t) by the equation y(t) = g(St - oof[x(tau)] h [t, tau, x (tau)]d tau). In words, some transformation f[x (t)] of the stimulus intensity is weighted by a function h and integrated; the result is transformed into the internal percept by a function g. This system postulates a linear integral operator preceded and followed by transformations which may be nonlinear. Based on forward masking of clicks by white noise, we (1) show that the above characterization of the model is appropriate (which involves showing that there is a linear temporal summation stage), and (2) derive certain characteristics of the system's nonlinearities. In particular, the integral of h times f is shown to be a nonlinear function of the input intensity exhibiting more compression than a power function. It is also shown that h must depend upon the intensity of the stimulus.