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scipy.signal.

# gammatone

scipy.signal.gammatone(freq, ftype, order=None, numtaps=None, fs=None, *, xp=None, device=None)

  Gammatone filter design.

  This function computes the coefficients of an FIR or IIR gammatone digital filter [1].

  Parameters:
    freq float

      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.

    order int, 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.

    numtaps int, 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.

    fs float, optional

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

    xp array_namespace, optional

      Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: `numpy`

    device: any

      optional device specification for output. Should match one of the supported device specification in `xp`.

  Returns:
    b, a ndarray, 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'`

  See also

  `firwin`
  `iirfilter`

  Notes

  Array API Standard Support

  `gammatone` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  > See Support for the array API standard for more information.

  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

      >>> import matplotlib.pyplot as plt
      >>> import numpy as np

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