Over the last half century, many auditory filter models have been developed, analyzed, and applied to hearing-related problems. Linear filter models, along with more realistic quasi-linear level-dependent models, have been explored. We review several lines of development, and several criteria that filter models might try to satisfy, and show how the pole–zero filter cascade (PZFC) models achieve these desired properties.

Early attempts at describing auditory function by filters used three kinds of filter shapes: simple resonances, Gaussian filters, and rectangular filters. Most more modern auditory filter models can be seen as belonging to three main families (detailed in Section 13.4.1): the rounded exponential (roex) family, the gammatone family, and the filter cascade family. In many cases, independent efforts led to somewhat similar results, without necessarily sharing a name or any other relationship. I have discovered some of these relationships in retrospect, such as the early 1960s work by Jim Flanagan (1960, 1962) on gammatone, one-zero gammatone, and related pole– zero filter models of basilar membrane motion, long before the term gammatone was coined.

Transmission-line models of wave propagation on the basilar membrane go even further back, but the basis for approximating these systems as cascade-structured filter models was not made clear until after Zweig, Lipes, and Pierce (1976) showed how to apply theWentzel–Kramers–Brillouin (WKB) approximation in their 1976 “cochlear compromise” paper.