# scipy.signal.gammatone¶

scipy.signal.gammatone(freq, ftype, order=None, numtaps=None, fs=None)[source]

Gammatone filter design.

This function computes the coefficients of an FIR or IIR gammatone digital filter .

Parameters
freqfloat

Center frequency of the filter (expressed in the same units as fs).

ftype{‘fir’, ‘iir’}

The type of filter the function generates. If ‘fir’, the function will generate an Nth order FIR gammatone filter. If ‘iir’, the function will generate an 8th order digital IIR filter, modeled as as 4th order gammatone filter.

orderint, optional

The order of the filter. Only used when `ftype='fir'`. Default is 4 to model the human auditory system. Must be between 0 and 24.

numtapsint, optional

Length of the filter. Only used when `ftype='fir'`. Default is `fs*0.015` if fs is greater than 1000, 15 if fs is less than or equal to 1000.

fsfloat, optional

The sampling frequency of the signal. freq must be between 0 and `fs/2`. Default is 2.

Returns
b, andarray, ndarray

Numerator (`b`) and denominator (`a`) polynomials of the filter.

Raises
ValueError

If freq is less than or equal to 0 or greater than or equal to `fs/2`, if ftype is not ‘fir’ or ‘iir’, if order is less than or equal to 0 or greater than 24 when `ftype='fir'`

References

1

Slaney, Malcolm, “An Efficient Implementation of the Patterson-Holdsworth Auditory Filter Bank”, Apple Computer Technical Report 35, 1993, pp.3-8, 34-39.

Examples

16-sample 4th order FIR Gammatone filter centered at 440 Hz

```>>> from scipy import signal
>>> signal.gammatone(440, 'fir', numtaps=16, fs=16000)
(array([ 0.00000000e+00,  2.22196719e-07,  1.64942101e-06,  4.99298227e-06,
1.01993969e-05,  1.63125770e-05,  2.14648940e-05,  2.29947263e-05,
1.76776931e-05,  2.04980537e-06, -2.72062858e-05, -7.28455299e-05,
-1.36651076e-04, -2.19066855e-04, -3.18905076e-04, -4.33156712e-04]),
[1.0])
```

IIR Gammatone filter centered at 440 Hz

```>>> from scipy import signal
>>> import matplotlib.pyplot as plt
```
```>>> b, a = signal.gammatone(440, 'iir', fs=16000)
>>> w, h = signal.freqz(b, a)
>>> plt.plot(w / ((2 * np.pi) / 16000), 20 * np.log10(abs(h)))
>>> plt.xscale('log')
>>> plt.title('Gammatone filter frequency response')
>>> plt.xlabel('Frequency')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.margins(0, 0.1)
>>> plt.grid(which='both', axis='both')
>>> plt.axvline(440, color='green') # cutoff frequency
>>> plt.show()
``` 