Module « scipy.signal »

Fonction bilinear_zpk - module scipy.signal

Signature de la fonction bilinear_zpk

def bilinear_zpk(z, p, k, fs) 

Description

bilinear_zpk.__doc__

    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
    ----------
    z : array_like
        Zeros of the analog filter transfer function.
    p : array_like
        Poles of the analog filter transfer function.
    k : float
        System gain of the analog filter transfer function.
    fs : float
        Sample rate, as ordinary frequency (e.g., hertz). No prewarping is
        done in this function.

    Returns
    -------
    z : ndarray
        Zeros of the transformed digital filter transfer function.
    p : ndarray
        Poles of the transformed digital filter transfer function.
    k : float
        System gain of the transformed digital filter.

    See Also
    --------
    lp2lp_zpk, lp2hp_zpk, lp2bp_zpk, lp2bs_zpk
    bilinear

    Notes
    -----
    .. versionadded:: 1.1.0

    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,
    ...                                   output='zpk'))
    >>> filtz = signal.lti(*signal.bilinear_zpk(filts.zeros, filts.poles,
    ...                                         filts.gain, fs))
    >>> wz, hz = signal.freqz_zpk(filtz.zeros, filtz.poles, filtz.gain)
    >>> ws, hs = signal.freqs_zpk(filts.zeros, filts.poles, filts.gain,
    ...                           worN=fs*wz)
    >>> plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hz).clip(1e-15)),
    ...              label=r'$|H_z(e^{j \omega})|$')
    >>> plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hs).clip(1e-15)),
    ...              label=r'$|H(j \omega)|$')
    >>> plt.legend()
    >>> plt.xlabel('Frequency [Hz]')
    >>> plt.ylabel('Magnitude [dB]')
    >>> plt.grid()