Nonlinear, nonlocal two dimensional cochlear modeling : efficient implementation and model order reduction

Abstract

Auditory signal analysis is traditionally addressed using an ever growing set of tools derived from signal processing area. Early on, frequency decomposition into biologically-relevant bands, the Mel frequencies, took hold as a natural first step in efficiently dividing an auditory signal into sensory-relevant components. The cochlear response, however, is considerably more complicated due to the nonlinear interaction between the local resonant hair cells, the perilymph, and the tectorial membrane, which cannot be understood using linear filter-bank decompositions of a given sound. Accordingly, cochlear modeling is a promising approach to, first, understanding nonlinear mixing of sounds, and second, developing more efficient auditory signal processing tools. In this thesis, we develop computationally efficient reduced order models of cochlear responses. An existing 2-space dimensional, nonlinear, nonlocal cochlear model is reviewed and transformed into a state space realization. Recasting the system accordingly renders it in a compact representation which allows an easy study of frequency response, stability analysis and system tuning. First, the model is formulated in a linear regime where the active gain is preset as a constant. Then, the active gain is allowed to vary in a nonlinear, nonlocal fashion. Furthermore, the system in its linear regime is employed to perform a model order reduction using a balancing transformation. Finally, the resulting transformation is used to extend the model order reduction to the nonlinear regime. Mathematically, the matrices are manipulated to achieve fast computations and high accuracy using common solving tools. As a matter of fact, the efficient implementation reduced the computational burden to the order of 30 times.