Gammatone Filter

A gammatone filter is a linear filter described by an impulse response that is the product of a gamma distribution and sinusoidal tone. It is a widely used model of auditory filters in the auditory system.

The gammatone impulse response is given by

where is the frequency, is the phase of the carrier, is the amplitude, is the filter's order, is the filter's bandwidth, and is time.

This is a sinusoid (a pure tone) with an amplitude envelope which is a scaled gamma distribution function.