   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.

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

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()
rp