scipy.signal.bilinear

scipy.signal.bilinear(b, a, fs=1.0)

Return a digital IIR filter from an analog one using a bilinear transform.

Transform a set of poles and zeros from the analog s-plane to the digital z-plane using Tustin’s method, which substitutes (z-1) / (z+1) for s, maintaining the shape of the frequency response.

Parameters

barray_like

Numerator of the analog filter transfer function.

aarray_like

Denominator of the analog filter transfer function.

fsfloat

Sample rate, as ordinary frequency (e.g. hertz). No prewarping is done in this function.

Returns

zndarray

Numerator of the transformed digital filter transfer function.

pndarray

Denominator of the transformed digital filter transfer function.

See also

lp2lp, lp2hp, lp2bp, lp2bs

bilinear_zpk

Examples

>>> from scipy import signal
>>> import matplotlib.pyplot as plt

>>> fs = 100
>>> bf = 2 * np.pi * np.array([7, 13])
>>> filts = signal.lti(*signal.butter(4, bf, btype='bandpass', analog=True))
>>> filtz = signal.lti(*signal.bilinear(filts.num, filts.den, fs))
>>> wz, hz = signal.freqz(filtz.num, filtz.den)
>>> ws, hs = signal.freqs(filts.num, filts.den, worN=fs*wz)

>>> plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hz).clip(1e-15)), label=r'$|H(j \omega)|$')
>>> plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hs).clip(1e-15)), label=r'$|H_z(e^{j \omega})|$')
>>> plt.legend()
>>> plt.xlabel('Frequency [Hz]')
>>> plt.ylabel('Magnitude [dB]')
>>> plt.grid()