GAMMATONE - Gammatone filter coefficients

  • [b,a] = gammatone(fc,fs,n,betamul);
  • [b,a] = gammatone(fc,fs,n);
  • [b,a] = gammatone(fc,fs);
Input parameters:
  • fc - center frequency in Hz.
  • fs - sampling rate in Hz.
  • n - filter order.
  • beta - bandwidth of the filter.
Output parameters:
  • b - nominator coefficients.
  • a - denominator coefficients.


GAMMATONE(fc,fs,n,betamul) computes the filter coefficients of a digital gammatone filter with center frequency fc, order n, 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.

GAMMATONE(fc,fs,n) will do the same but choose a filter bandwidth according to Glasberg and Moore (1990). The order n can only be 2 or 4. If the order is 4 then betamul is choosen to be 1.0183 and if the order is 2 then betamul is choosen to be 0.637.

GAMMATONE(fc,fs) will do as above for a 4th order filter.

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

The inpulse response of the gammatone filter is given by
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
    [b,a] = gammatone(fs,erbspacebw(flow,fhigh));


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