GAMMATONEFIR - Gammatone filter coefficients

Usage

b = gammatonefir(fc,fs,n,betamul);
b = gammatonefir(fc,fs,n);
b = gammatonefir(fc,fs);

Input parameters

`fc`	center frequency in Hz.
`fs`	sampling rate in Hz.
`n`	max. filter length.
`beta`	bandwidth of the filter.

Output parameters

`b`	FIR filters as an cell-array of structs.

Description

gammatonefir(fc,fs,n,betamul) computes the filter coefficients of a digital FIR gammatone filter with length at most n, center frequency fc, 4th order rising slope, sampling rate fs and bandwith determined by betamul. The bandwidth beta of each filter is determined as betamul times audfiltbw of the center frequency of corresponding filter. The actual length of the inpulse response depends on fc (the filter is longer for low center frequencies), fs and betamul but it is never bigger than n.

gammatonefir(fc,fs,n) will do the same but choose a filter bandwidth according to Glasberg and Moore (1990). betamul is choosen to be 1.0183.

gammatonefir(fc,fs) will do as above and choose a sufficiently long filter to accurately represent the lowest subband channel.

If fc is a vector, each entry of fc is considered as one center frequency, and the corresponding coefficients are returned as column vectors in the output.

The inpulse response of the gammatone filter is given by

\begin{equation*} g(t) = at^{4-1}cos(2\pi\cdot fc\cdot t)e^{-2\pi \beta \cdot t} \end{equation*}

The gammatone filters as implemented by this function generate complex valued output, because the filters are modulated by the exponential function. Using real on the output will give the coefficients of the corresponding cosine modulated filters.

To create the filter coefficients of a 1-erb spaced filter bank using gammatone filters use the following construction:

g = gammatonefir(erbspacebw(flow,fhigh),fs);

References:

A. Aertsen and P. Johannesma. Spectro-temporal receptive fields of auditory neurons in the grassfrog. I. Characterization of tonal and natural stimuli. Biol. Cybern, 38:223--234, 1980.

B. R. Glasberg and B. Moore. Derivation of auditory filter shapes from notched-noise data. Hearing Research, 47(1-2):103, 1990.