I have long viewed the automatic gain control (AGC) function as one of the most important, and tricky, parts of modeling the function of the cochlea (Lyon, 1982, 1990). To understand or design this important level-adaptive function, one must have an appreciation for the dynamics of feedback control, in a highly variable nonlinear context.

In this chapter, I provide the basic background and analysis techniques that our cochlear models will draw on. In particular, I show how the use of output amplitude to control the damping factors of cascaded resonators can be modeled as a robust feedback control system that compresses a wide input dynamic range into a narrower output dynamic range, by examining this approach in the context of a fairly general single-channel AGC formulation.

Input–Output Level Compression

Systems that use feedback from a detected output level to adjust their own parameters to keep the output level from varying too much are called automatic gain control systems. Such systems are inherently nonlinear, with a compressive input–output function: when the input changes by some factor, the output level changes by a factor closer to 1. AGC has long been used and analyzed in wireless communication systems (Wheeler, 1928; Küpfmüller, 1928), including television (De Forest, 1942), and is an idea that has long inspired corresponding models in biological systems, including vision and hearing (Rose, 1948, 1973; Smith and Zwislocki, 1975; Allen, 1979).