A gammatone is the product of a rising polynomial, a decaying exponential function, and a cosine wave.

It can be described with the following formula:

gammaTone (*t*) = *a* *t*^{γ–1} e^{–2π·bandwidth·t} cos (2*π·frequency·t* + *initialPhase*), |

where γ determines the order of the gammatone.

The gammatone function has a monotone carrier (the tone) with an envelope that is a gamma distribution function. The amplitude spectrum is essentially symmetric on a linear frequency scale. This function is used in some time-domain auditory models to simulate the spectral analysis performed by the basilar membrane. It was popularized in auditory modeling by Johannesma (1972). Flanagan (1960) already used it to model basilar membrane motion.

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© djmw, May 17, 2010