Gammatone filter

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Figure 1: A gammatone impulse response.

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

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

where f (in Hz) is the center frequency, \phi (in radians) is the phase of the carrier, a is the amplitude, n is the filter's order, b (in Hz) is the filter's bandwidth, and t (in seconds) is time.

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


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]


  1. ^ Slaney, Malcolm (1993). "An Efficient Implementation of the Patterson-Holdsworth Auditory Filter Bank" (PDF). Apple Computer Technical Report #35. 
  2. ^ Richard F. Lyon, Andreas G. Katsiamis, Emmanuel M. Drakakis (2010). "History and Future of Auditory Filter Models" (PDF). Proc. ISCAS. IEEE. 

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