The cochlea is the ear's sound filtering and amplification system, consisting primarily of two fluid-filled channels, the membrane that separates them, and the tiny organ of Corti that sits along the edge of the membrane to amplify and detect motion.

How can we describe and replicate what the cochlea does? By models—especially by models that have a structure derived from the underlying physics and that have been validated against a range of measurements on real human and animal auditory systems. Models that are based on distributed linear system theory, plus appropriate nonlinearities, describe the cochlea well, and lead to efficient algorithms or machines that can replicate the cochlea's sound analysis function.

The system theory that we reviewed through Chapter 12 is all relevant—nonlinear, gain-controlled, distributed resonance-like filtering. We may conceptually look at the system response as an infinite number of outputs, at a continuum of locations, each representing a different nonlinear system—or more productively, we can focus on how the different locations build on each other, and make a more powerful and compact model through that approach.

In the cochlea, the membrane interacts with the fluid, constrained by the shape of the channel, to make a transmission line that supports mechanical traveling waves. Positions along this transmission line correspond to a large number of outputs, with a progression of different frequency responses, analogous to the old Helmholtz resonance view of cochlear function. As we emphasized before, the cochlea has important linear and nonlinear aspects; it even acts as a distributed amplifier, and adds energy to traveling waves to boost the response to weak sounds.