To model the active and compressive amplifying wave propagation in the cochlea, the CARFAC stage incorporates dynamic nonlinearity or fast acting compression (FAC) through a structure we call the digital outer hair cell (DOHC), shown in Figure 17.1. This structure varies the positions of the poles and zeros, changing their radius r in the z plane by changing r in the coefficient formulas. The r value is increased from its passive value, where it would be for very loud sounds, to actively reduce damping for weaker sounds. Alternatively, we may say that the r value is decreased in response to sound, from its maximum value in quiet, down to a minimum or passive value.

Compression of a wide input dynamic range, by controlling the amplification of lowlevel sounds, is the primary function of this component, which is unique to the mammalian auditory system. The distortion that the OHC generates as an inevitable byproduct of varying the gain is useful as a diagnostic, both for humans and for machine models. The distortion products are sometimes audible, contributing to perceptual differences between sounds.

The cell-membrane protein channel that makes outer hair cells work as active “motors” is known as prestin. Species with good high-frequency echolocation capabilities—bats and dolphins—exhibit an interesting convergent evolution of their prestin genes, presumably in support of good high-frequency amplification of feeble echos (Li et al., 2010).