Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interactions in Hearing

J. Xin, Y. Qi, and Li Deng

Abstract

A nonlinear, nonlocal cochlear model of the transmission line type is studied in

order to capture the multitone interactions and resulting tonal suppression effects. The model can

serve as a module for voice signal processing, and is a one-dimensional (in space) damped dispersive

nonlinear PDE based on the mechanics and phenomenology of hearing. It describes the motion of

the basilar membrane (BM) in the cochlea driven by input pressure waves. Both elastic damping

and selective longitudinal fluid damping are present. The former is nonlinear and nonlocal in BM

displacement, and plays a key role in capturing tonal interactions. The latter is active only near

the exit boundary (helicotrema), and is built in to damp out the remaining long waves. The initial

boundary value problem is numerically solved with a semi-implicit second order finite difference

method. Solutions reach a multi-frequency quasi-steady state. Numerical results are shown on two

tone suppression from both high-frequency and low-frequency sides, consistent with known behavior

of two tone suppression. Suppression effects among three tones are demonstrated by showing how

the response magnitudes of the fixed two tones are reduced as we vary the third tone in frequency

and amplitude. We observe qualitative agreement of our model solutions with existing cat auditory

neural data. The model is thus a simple and efficient processing tool for voice signals.

Details

Publication typeArticle
Published inCommunications in Mathematical Sciences
Pages211-227
Volume1
Number2
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