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