def window_cauchy(N, alpha=<NUM_LIT:3>):
n = linspace(-N/<NUM_LIT>, (N)/<NUM_LIT>, N)<EOL>w = <NUM_LIT:1.>/(<NUM_LIT:1.>+ (alpha*n/(N/<NUM_LIT>))**<NUM_LIT:2>)<EOL>return w<EOL>
r"""Cauchy tapering window

    :param int N: window length
    :param float alpha: parameter of the poisson window

    .. math:: w(n) = \frac{1}{1+\left(\frac{\alpha*n}{N/2}\right)**2}

    .. plot::
        :width: 80%
        :include-source:

        from spectrum import window_visu
        window_visu(64, 'cauchy', alpha=3)
        window_visu(64, 'cauchy', alpha=4)
        window_visu(64, 'cauchy', alpha=5)


    .. seealso:: :func:`window_poisson`, :func:`window_hann`