code: def window_cauchy(N, alpha=3):
      r
      n = linspace(-N/2., (N)/2., N)
      w = 1./(1.+ (alpha*n/(N/2.))**2)
      return w
docs: 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`