Signal processing in the cochlea: The structure equations

Abstract

BACKGROUND: Physical and physiological invariance laws, in particular time invariance and local symmetry, are at the outset of an abstract model. Harmonic analysis and Lie theory are the mathematical prerequisites for its deduction.RESULTS: The main result is a linear system of partial differential equations (referred to as the structure equations) that describe the result of signal processing in the cochlea. It is formulated for phase and for the logarithm of the amplitude. The changes of these quantities are the essential physiological observables in the description of signal processing in the auditory pathway.CONCLUSIONS: The structure equations display in a quantitative way the subtle balance for processing information on the basis of phase versus amplitude. From a mathematical point of view, the linear system of equations is classified as an inhomogeneous ∂¯-equation. In suitable variables the solutions can be represented as the superposition of a particular solution (determined by the system) and a holomorphic function (determined by the incoming signal). In this way, a global picture of signal processing in the cochlea emerges.