Module « scipy.signal »

Fonction freqz_zpk - module scipy.signal

Signature de la fonction freqz_zpk

def freqz_zpk(z, p, k, worN=512, whole=False, fs=6.283185307179586) 

Description

freqz_zpk.__doc__

    Compute the frequency response of a digital filter in ZPK form.

    Given the Zeros, Poles and Gain of a digital filter, compute its frequency
    response:

    :math:`H(z)=k \prod_i (z - Z[i]) / \prod_j (z - P[j])`

    where :math:`k` is the `gain`, :math:`Z` are the `zeros` and :math:`P` are
    the `poles`.

    Parameters
    ----------
    z : array_like
        Zeroes of a linear filter
    p : array_like
        Poles of a linear filter
    k : scalar
        Gain of a linear filter
    worN : {None, int, array_like}, optional
        If a single integer, then compute at that many frequencies (default is
        N=512).

        If an array_like, compute the response at the frequencies given.
        These are in the same units as `fs`.
    whole : bool, optional
        Normally, frequencies are computed from 0 to the Nyquist frequency,
        fs/2 (upper-half of unit-circle). If `whole` is True, compute
        frequencies from 0 to fs. Ignored if w is array_like.
    fs : float, optional
        The sampling frequency of the digital system. Defaults to 2*pi
        radians/sample (so w is from 0 to pi).

        .. versionadded:: 1.2.0

    Returns
    -------
    w : ndarray
        The frequencies at which `h` was computed, in the same units as `fs`.
        By default, `w` is normalized to the range [0, pi) (radians/sample).
    h : ndarray
        The frequency response, as complex numbers.

    See Also
    --------
    freqs : Compute the frequency response of an analog filter in TF form
    freqs_zpk : Compute the frequency response of an analog filter in ZPK form
    freqz : Compute the frequency response of a digital filter in TF form

    Notes
    -----
    .. versionadded:: 0.19.0

    Examples
    --------
    Design a 4th-order digital Butterworth filter with cut-off of 100 Hz in a
    system with sample rate of 1000 Hz, and plot the frequency response:

    >>> from scipy import signal
    >>> z, p, k = signal.butter(4, 100, output='zpk', fs=1000)
    >>> w, h = signal.freqz_zpk(z, p, k, fs=1000)

    >>> import matplotlib.pyplot as plt
    >>> fig = plt.figure()
    >>> ax1 = fig.add_subplot(1, 1, 1)
    >>> ax1.set_title('Digital filter frequency response')

    >>> ax1.plot(w, 20 * np.log10(abs(h)), 'b')
    >>> ax1.set_ylabel('Amplitude [dB]', color='b')
    >>> ax1.set_xlabel('Frequency [Hz]')
    >>> ax1.grid()

    >>> ax2 = ax1.twinx()
    >>> angles = np.unwrap(np.angle(h))
    >>> ax2.plot(w, angles, 'g')
    >>> ax2.set_ylabel('Angle [radians]', color='g')

    >>> plt.axis('tight')
    >>> plt.show()