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[[File:Sample gammatone.svg|thumb|right|'''Figure 1:''' A gammatone impulse response.]]
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A '''gammatone filter''' is a [[linear filter]] described by an [[impulse response]] that is the product of a [[gamma distribution]] and [[Sine wave|sinusoid]]al tone. It is a widely used model of [[auditory filters]] in the [[auditory system]].
 
The gammatone impulse response is given by
 
:<math>
g(t) = at^{n-1} e^{-2\pi bt} \cos(2\pi ft + \phi), \,
</math>
 
where
<math>f</math> (in Hz) is the center frequency,
<math>\phi</math> (in [[radians]]) is the phase of the carrier,
<math>a</math> is the amplitude,
<math>n</math> is the filter's order,
<math>b</math> (in Hz) is the filter's bandwidth, and
<math>t</math> (in seconds) is time.
 
This is a sinusoid (a [[pure tone]]) with an amplitude envelope which is a scaled [[gamma distribution]] function.<ref>
{{cite web
| url = http://rvl4.ecn.purdue.edu/%7Emalcolm/apple/tr35/PattersonsEar.pdf
| author = Slaney, Malcolm
| title = An Efficient Implementation of the Patterson-Holdsworth Auditory Filter Bank
| publisher = Apple Computer Technical Report #35
| year = 1993
}}</ref>
 
==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.<ref>
{{cite web
| title = History and Future of Auditory Filter Models
| url = http://research.google.com/pubs/archive/36895.pdf
| work = Proc. ISCAS
| author = Richard F. Lyon, Andreas G. Katsiamis, Emmanuel M. Drakakis
| publisher = IEEE
| date = 2010
}}</ref>
 
==References==
 
{{reflist}}
 
== External links ==
* [http://library.wolfram.com/infocenter/MathSource/2052/#downloads Slaney's implementation in Mathematica]
* [http://www.dcs.shef.ac.uk/~ning/resources/gammatone/ Cooke's implementation in C]
* [http://lumiere.ens.fr/Audition/tools/realtime/ A real-time implementation in C++ (for PureData)]
 
[[Category:Auditory system]]
[[Category:Linear filters]]
 
 
{{neuroscience-stub}}

Revision as of 06:35, 10 February 2014

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