Module « scipy.signal »

Fonction sosfreqz - module scipy.signal

Signature de la fonction sosfreqz

def sosfreqz(sos, worN=512, whole=False, fs=6.283185307179586) 

Description

sosfreqz.__doc__

    Compute the frequency response of a digital filter in SOS format.

    Given `sos`, an array with shape (n, 6) of second order sections of
    a digital filter, compute the frequency response of the system function::

               B0(z)   B1(z)         B{n-1}(z)
        H(z) = ----- * ----- * ... * ---------
               A0(z)   A1(z)         A{n-1}(z)

    for z = exp(omega*1j), where B{k}(z) and A{k}(z) are numerator and
    denominator of the transfer function of the k-th second order section.

    Parameters
    ----------
    sos : array_like
        Array of second-order filter coefficients, must have shape
        ``(n_sections, 6)``. Each row corresponds to a second-order
        section, with the first three columns providing the numerator
        coefficients and the last three providing the denominator
        coefficients.
    worN : {None, int, array_like}, optional
        If a single integer, then compute at that many frequencies (default is
        N=512).  Using a number that is fast for FFT computations can result
        in faster computations (see Notes of `freqz`).

        If an array_like, compute the response at the frequencies given (must
        be 1-D). 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.
    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
    --------
    freqz, sosfilt

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

    Examples
    --------
    Design a 15th-order bandpass filter in SOS format.

    >>> from scipy import signal
    >>> sos = signal.ellip(15, 0.5, 60, (0.2, 0.4), btype='bandpass',
    ...                    output='sos')

    Compute the frequency response at 1500 points from DC to Nyquist.

    >>> w, h = signal.sosfreqz(sos, worN=1500)

    Plot the response.

    >>> import matplotlib.pyplot as plt
    >>> plt.subplot(2, 1, 1)
    >>> db = 20*np.log10(np.maximum(np.abs(h), 1e-5))
    >>> plt.plot(w/np.pi, db)
    >>> plt.ylim(-75, 5)
    >>> plt.grid(True)
    >>> plt.yticks([0, -20, -40, -60])
    >>> plt.ylabel('Gain [dB]')
    >>> plt.title('Frequency Response')
    >>> plt.subplot(2, 1, 2)
    >>> plt.plot(w/np.pi, np.angle(h))
    >>> plt.grid(True)
    >>> plt.yticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi],
    ...            [r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
    >>> plt.ylabel('Phase [rad]')
    >>> plt.xlabel('Normalized frequency (1.0 = Nyquist)')
    >>> plt.show()

    If the same filter is implemented as a single transfer function,
    numerical error corrupts the frequency response:

    >>> b, a = signal.ellip(15, 0.5, 60, (0.2, 0.4), btype='bandpass',
    ...                    output='ba')
    >>> w, h = signal.freqz(b, a, worN=1500)
    >>> plt.subplot(2, 1, 1)
    >>> db = 20*np.log10(np.maximum(np.abs(h), 1e-5))
    >>> plt.plot(w/np.pi, db)
    >>> plt.ylim(-75, 5)
    >>> plt.grid(True)
    >>> plt.yticks([0, -20, -40, -60])
    >>> plt.ylabel('Gain [dB]')
    >>> plt.title('Frequency Response')
    >>> plt.subplot(2, 1, 2)
    >>> plt.plot(w/np.pi, np.angle(h))
    >>> plt.grid(True)
    >>> plt.yticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi],
    ...            [r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
    >>> plt.ylabel('Phase [rad]')
    >>> plt.xlabel('Normalized frequency (1.0 = Nyquist)')
    >>> plt.show()