Stationary noise responses in a nonlinear model of cochlear mechanics: iterative solutions in the frequency domain

To examine quasilinear filtering properties in cochlear mechanics, Liu and Neely [(2012). What Fire is in Mine Ears: Progress in Auditory Biomechanics, edited by C. A. Shera and E. S. Olson (AIP, Melville, NY), pp. 218-223] calculated Wiener kernels of a nonlinear cochlear model; it was verified that the model's responses to noise could be accurately predicted by treating the kernels as the impulse responses of an equivalent linear system. However, this previous work fell short of showing that the quasilinear filters could be realized under the same structure of the model, a property predicted by de Boer [(1997). Aud. Neurosci. 3, 377-388]. To address the issue of realizability, this paper presents a method that computes the cochlear model's responses to noise iteratively in the frequency domain. First, cochlear transfer functions are calculated as if the system is linear; then, the efficiency of the outer hair cell electromechanical transduction is adjusted. The two steps repeat until the transfer functions converge. Simulation shows that, as the stimulus level increases, the magnitude response of the cochlea decreases and the latency shortens. The corresponding impulse responses are approximately equal to the Wiener kernels obtained in time-domain simulation; as the stimulus varies, the approximation error is <5% in terms of energy. Thus, the Wiener kernels are effectively computed via the present method, which guarantees that the structure of the model is preserved.