Bandpass Filters

Auditory filtering in the cochlea is generally conceptualized as bandpass filtering, with a dense array of filters representing up to thousands of locations along the cochlear partition. A bandpass filter is a system that responds strongly to frequency components within its passband, and only weakly to signals of other frequencies. This concept came up in the context of critical bands, and in the context of spectrum analysis; now we proceed to the mathematical description of the concept, building on what we learned about general linear systems in previous chapters.

We often refer to the peak of a bandpass filter; the peak frequency (or center frequency) and peak gain describe the point of highest gain, while the peak width and peak shape describe the frequency response of the passband, the high part of the frequency response close to that point. The parts of the frequency response further from the peak are often described as the skirt or tails of the bandpass response—often skirt if it drops rapidly, as a transition to a stopband, a range of frequencies in which the filter attenuates strongly, and tail if the frequency response levels off or drops slowly. This tail terminology appears to be unique to the hearing field, in which the low-frequency tails of tuning curves have long been recognized as functionally important (Kiang and Moxon, 1974).