signal.py 文件源码

def lorentz(M, std=1.0, sym=True):
    """Lorentz window (same as Cauchy function). Function skeleton stolen from
    scipy.signal.gaussian().

    The Lorentz function is

    .. math:: 

        L(x) = \\frac{\Gamma}{(x-x_0)^2 + \Gamma^2}

    Here :math:`x_0 = 0` and `std` = :math:`\Gamma`.
    Some definitions use :math:`1/2\,\Gamma` instead of :math:`\Gamma`, but
    without 1/2 we get comparable peak width to Gaussians when using this
    window in convolutions, thus ``scipy.signal.gaussian(M, std=5)`` is similar
    to ``lorentz(M, std=5)``.

    Parameters
    ----------
    M : int
        number of points
    std : float 
        spread parameter :math:`\Gamma`
    sym : bool

    Returns
    -------
    w : (M,)
    """
    if M < 1:
        return np.array([])
    if M == 1:
        return np.ones(1,dtype=float)
    odd = M % 2
    if not sym and not odd:
        M = M+1
    n = np.arange(0, M) - (M - 1.0) / 2.0
    w = std / (n**2.0 + std**2.0)
    w /= w.max()
    if not sym and not odd:
        w = w[:-1]
    return w