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.