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

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

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.

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

References

[http://rvl4.ecn.purdue.edu/%7Emalcolm/apple/tr35/PattersonsEar.pdf Slaney, Malcolm, "An Efficient Implementation of the Patterson-Holdsworth Auditory Filter Bank," Apple Computer Technical Report #35, Perception Group—Advanced Technology Group (1993).]

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]