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 center 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 with an amplitude envelope which is a scaled gamma distribution function.
Different ways of motivating the gammatone filter for auditory processing have been presented by
Johannesma,
Patterson et al.,
Hewitt and Meddis,
and Lindeberg and Friberg.

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.