A discrete time parametric model of auditory filters at peak sensitivity

Abstract

The first stage of human auditory processing is the filtration performed by the ear. The middle ear, basilar membrane, and tectorial membrane contribute to a filter bank specialized for amplitude and frequency selectivity. Accurately modeling this system is of critical importance, because the properties of the cochlear filter bank determine what audio information is available to humans. Because the cochlea is such an intricate and non-linear system, many cochlear models are computationally taxing and unusable for real time applications. By making a judicious linear approximation of the system, digital filters modeled after the cochlea can be implemented efficiently in real time. However, the digital filter models presently in use (often eighth order gammatone or elliptic filters) do a poor job of capturing the most perceptually critical properties of the cochlear filter bank. In this report, a set of parametric digital filters are proposed, which accurately model cochlear filters at peak sensitivity from 80 Hz to 19.5 kHz best frequency. The filters were designed using a gradient of steepest descent method to fit target frequency responses generated by a physical model of the cochlea. The final result is a set of polynomial equations which describe the locations of the poles and zeros of the digital cochlear filter approximations as a function of normalized cochlear best place.