Document Type

Dissertation

Degree

Doctor of Philosophy

Major

Applied Mathematics

Date of Defense

5-12-2014

Graduate Advisor

Charles Chui

Committee

Gary Miller

Henry Kang

Uday Chakraborty

Abstract

The human cochlea possesses the amazing ability of analyzing audio signals. The structures and mechanisms behind its characteristic response to sound stimuli has been an active area of research for decades. It has been demonstrated that mathematical cochlear modeling poses a promising alternative to discover the elusive activities in an in vivo cochlea. However, despite the successful application of numerical methods such as the Wentzel-Kramers-Brillouin (WKB) method, finite difference method (FDM) and finite element method (FEM), the critical effects of the choice of basis functions have not been studied exclusively for the numerical solutions of cochlea models. This work presents the numerical solution procedures to two types of cochlear models using the basis function collocation approach. Accuracies and effectiveness of basis functions are evaluated by comparing simulation results with past experiment and physiological data. The time-domain solutions in response to various audio inputs are also shown. The cochlear model demonstrates sound processing abilities which are qualitatively comparable to physiological data. It is hoped that the results in this work would help in laying the foundation for future cochlear model solutions and cochlea-based audio signal processor.

Included in

Mathematics Commons

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