Gammatone filter

A gammatone filter is an impulse response filter used in many models of the auditory system. It is the most widely used example of auditory filters. It is described by the equation



g(t) = at^{n-1}\cos(2\pi ft + \phi) e^{-2\pi bt}, \, $$

where $$f$$ is the frequency, $$\phi$$ is the phase of the carrier, $$a$$ is the amplitude, $$n$$ is the filter's order, $$b$$ is the filter's bandwidth, and $$t$$ is time.