Module « scipy.signal »

Fonction exponential - module scipy.signal

Signature de la fonction exponential

def exponential(*args, **kwargs) 

Description

exponential.__doc__

Return an exponential (or Poisson) window.

    .. warning:: scipy.signal.exponential is deprecated,
                 use scipy.signal.windows.exponential instead.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an empty
        array is returned.
    center : float, optional
        Parameter defining the center location of the window function.
        The default value if not given is ``center = (M-1) / 2``.  This
        parameter must take its default value for symmetric windows.
    tau : float, optional
        Parameter defining the decay.  For ``center = 0`` use
        ``tau = -(M-1) / ln(x)`` if ``x`` is the fraction of the window
        remaining at the end.
    sym : bool, optional
        When True (default), generates a symmetric window, for use in filter
        design.
        When False, generates a periodic window, for use in spectral analysis.

    Returns
    -------
    w : ndarray
        The window, with the maximum value normalized to 1 (though the value 1
        does not appear if `M` is even and `sym` is True).

    Notes
    -----
    The Exponential window is defined as

    .. math::  w(n) = e^{-|n-center| / \tau}

    References
    ----------
    .. [1] S. Gade and H. Herlufsen, "Windows to FFT analysis (Part I)",
           Technical Review 3, Bruel & Kjaer, 1987.

    Examples
    --------
    Plot the symmetric window and its frequency response:

    >>> from scipy import signal
    >>> from scipy.fft import fft, fftshift
    >>> import matplotlib.pyplot as plt

    >>> M = 51
    >>> tau = 3.0
    >>> window = signal.windows.exponential(M, tau=tau)
    >>> plt.plot(window)
    >>> plt.title("Exponential Window (tau=3.0)")
    >>> plt.ylabel("Amplitude")
    >>> plt.xlabel("Sample")

    >>> plt.figure()
    >>> A = fft(window, 2048) / (len(window)/2.0)
    >>> freq = np.linspace(-0.5, 0.5, len(A))
    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
    >>> plt.plot(freq, response)
    >>> plt.axis([-0.5, 0.5, -35, 0])
    >>> plt.title("Frequency response of the Exponential window (tau=3.0)")
    >>> plt.ylabel("Normalized magnitude [dB]")
    >>> plt.xlabel("Normalized frequency [cycles per sample]")

    This function can also generate non-symmetric windows:

    >>> tau2 = -(M-1) / np.log(0.01)
    >>> window2 = signal.windows.exponential(M, 0, tau2, False)
    >>> plt.figure()
    >>> plt.plot(window2)
    >>> plt.ylabel("Amplitude")
    >>> plt.xlabel("Sample")