Function bartlett

numpy/lib/_function_base_impl.py:3149–3252

Return the Bartlett window. The Bartlett window is very similar to a triangular window, except that the end points are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain. Parameters --------

(M)

@set_module('numpy')
def bartlett(M):
    """
    Return the Bartlett window.

    The Bartlett window is very similar to a triangular window, except
    that the end points are at zero.  It is often used in signal
    processing for tapering a signal, without generating too much
    ripple in the frequency domain.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.

    Returns
    -------
    out : array
        The triangular window, with the maximum value normalized to one
        (the value one appears only if the number of samples is odd), with
        the first and last samples equal to zero.

    See Also
    --------
    blackman, hamming, hanning, kaiser

    Notes
    -----
    The Bartlett window is defined as

    .. math:: w(n) = \\frac{2}{M-1} \\left(
              \\frac{M-1}{2} - \\left|n - \\frac{M-1}{2}\\right|
              \\right)

    Most references to the Bartlett window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  Note that convolution with this window produces linear
    interpolation.  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. The Fourier transform of the
    Bartlett window is the product of two sinc functions. Note the excellent
    discussion in Kanasewich [2]_.

    References
    ----------
    .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra",
           Biometrika 37, 1-16, 1950.
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
           The University of Alberta Press, 1975, pp. 109-110.
    .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal
           Processing", Prentice-Hall, 1999, pp. 468-471.
    .. [4] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function
    .. [5] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
           "Numerical Recipes", Cambridge University Press, 1986, page 429.

    Examples
    --------