def bartlett(M, sym=True):
<EOL>if M < <NUM_LIT:1>:<EOL><INDENT>return np.array([])<EOL><DEDENT>if M == <NUM_LIT:1>:<EOL><INDENT>return np.ones(<NUM_LIT:1>, '<STR_LIT:d>')<EOL><DEDENT>odd = M % <NUM_LIT:2><EOL>if not sym and not odd:<EOL><INDENT>M = M + <NUM_LIT:1><EOL><DEDENT>n = np.arange(<NUM_LIT:0>, M)<EOL>w = np.where(np.less_equal(n, (M - <NUM_LIT:1>) / <NUM_LIT>),<EOL><NUM_LIT> * n / (M - <NUM_LIT:1>), <NUM_LIT> - <NUM_LIT> * n / (M - <NUM_LIT:1>))<EOL>if not sym and not odd:<EOL><INDENT>w = w[:-<NUM_LIT:1>]<EOL><DEDENT>return w<EOL>
r"""
    Return a 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.
    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 triangular window, with the first and last samples equal to zero
        and the maximum value normalized to 1 (though the value 1 does not
        appear if `M` is even and `sym` is True).

    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 is the product
    of two sinc functions.
    Note the excellent discussion in Kanasewich.

    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",
           http://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
    --------
    Plot the window and its frequency response:

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

    >>> window = signal.bartlett(51)
    >>> plt.plot(window)
    >>> plt.title("Bartlett window")
    >>> 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("Frequency response of the Bartlett window")
    >>> plt.ylabel("Normalized magnitude [dB]")
    >>> plt.xlabel("Normalized frequency [cycles per sample]")