Module « scipy.signal »

Fonction kaiser - module scipy.signal

Signature de la fonction kaiser

def kaiser(*args, **kwargs) 

Description

kaiser.__doc__

Return a Kaiser window.

    The Kaiser window is a taper formed by using a Bessel function.

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

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an empty
        array is returned.
    beta : float
        Shape parameter, determines trade-off between main-lobe width and
        side lobe level. As beta gets large, the window narrows.
    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 Kaiser window is defined as

    .. math::  w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}}
               \right)/I_0(\beta)

    with

    .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2},

    where :math:`I_0` is the modified zeroth-order Bessel function.

    The Kaiser was named for Jim Kaiser, who discovered a simple approximation
    to the DPSS window based on Bessel functions.
    The Kaiser window is a very good approximation to the Digital Prolate
    Spheroidal Sequence, or Slepian window, which is the transform which
    maximizes the energy in the main lobe of the window relative to total
    energy.

    The Kaiser can approximate other windows by varying the beta parameter.
    (Some literature uses alpha = beta/pi.) [4]_

    ====  =======================
    beta  Window shape
    ====  =======================
    0     Rectangular
    5     Similar to a Hamming
    6     Similar to a Hann
    8.6   Similar to a Blackman
    ====  =======================

    A beta value of 14 is probably a good starting point. Note that as beta
    gets large, the window narrows, and so the number of samples needs to be
    large enough to sample the increasingly narrow spike, otherwise NaNs will
    be returned.

    Most references to the Kaiser window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function.

    References
    ----------
    .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by
           digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285.
           John Wiley and Sons, New York, (1966).
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
           University of Alberta Press, 1975, pp. 177-178.
    .. [3] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function
    .. [4] F. J. Harris, "On the use of windows for harmonic analysis with the
           discrete Fourier transform," Proceedings of the IEEE, vol. 66,
           no. 1, pp. 51-83, Jan. 1978. :doi:`10.1109/PROC.1978.10837`.

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

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

    >>> window = signal.windows.kaiser(51, beta=14)
    >>> plt.plot(window)
    >>> plt.title(r"Kaiser window ($\beta$=14)")
    >>> 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, -120, 0])
    >>> plt.title(r"Frequency response of the Kaiser window ($\beta$=14)")
    >>> plt.ylabel("Normalized magnitude [dB]")
    >>> plt.xlabel("Normalized frequency [cycles per sample]")