Module « scipy.signal »

Fonction group_delay - module scipy.signal

Signature de la fonction group_delay

def group_delay(system, w=512, whole=False, fs=6.283185307179586) 

Description

group_delay.__doc__

Compute the group delay of a digital filter.

    The group delay measures by how many samples amplitude envelopes of
    various spectral components of a signal are delayed by a filter.
    It is formally defined as the derivative of continuous (unwrapped) phase::

               d        jw
     D(w) = - -- arg H(e)
              dw

    Parameters
    ----------
    system : tuple of array_like (b, a)
        Numerator and denominator coefficients of a filter transfer function.
    w : {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 delay 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 group delay was computed, in the same units
        as `fs`.  By default, `w` is normalized to the range [0, pi)
        (radians/sample).
    gd : ndarray
        The group delay.

    Notes
    -----
    The similar function in MATLAB is called `grpdelay`.

    If the transfer function :math:`H(z)` has zeros or poles on the unit
    circle, the group delay at corresponding frequencies is undefined.
    When such a case arises the warning is raised and the group delay
    is set to 0 at those frequencies.

    For the details of numerical computation of the group delay refer to [1]_.

    .. versionadded:: 0.16.0

    See Also
    --------
    freqz : Frequency response of a digital filter

    References
    ----------
    .. [1] Richard G. Lyons, "Understanding Digital Signal Processing,
           3rd edition", p. 830.

    Examples
    --------
    >>> from scipy import signal
    >>> b, a = signal.iirdesign(0.1, 0.3, 5, 50, ftype='cheby1')
    >>> w, gd = signal.group_delay((b, a))

    >>> import matplotlib.pyplot as plt
    >>> plt.title('Digital filter group delay')
    >>> plt.plot(w, gd)
    >>> plt.ylabel('Group delay [samples]')
    >>> plt.xlabel('Frequency [rad/sample]')
    >>> plt.show()