# 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 (in Hz) is the center frequency, (in radians) is the phase of the carrier, is the amplitude, is the filter's order, (in Hz) is the filter's bandwidth, and (in seconds) is time.

This is a sinusoid (a pure tone) with an amplitude envelope which is a scaled gamma distribution function.^{[1]}

## Variations

Variations and improvements of the gammatone model of auditory filtering include the gammachirp filter, the all-pole and one-zero gammatone filters, the two-sided gammatone filter, and filter cascade models, and various level-dependent and dynamically nonlinear versions of these.^{[2]}