code: def exponential(M, center=None, tau=1.0, sym=True):
      r"""Return an exponential (or Poisson) window.
  
      Parameters
      ----------
      M : int
          Number of points in the output window. If zero or less, an empty
          array is returned.
      center : float, optional
          Parameter defining the center location of the window function.
          The default value if not given is ``center = (M-1) / 2``.  This
          parameter must take its default value for symmetric windows.
      tau : float, optional
          Parameter defining the decay.  For ``center = 0`` use
          ``tau = -(M-1) / ln(x)`` if ``x`` is the fraction of the window
          remaining at the end.
      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 Exponential window is defined as
  
      .. math::  w(n) = e^{-|n-center| / \tau}
  
      References
      ----------
      .. [1] S. Gade and H. Herlufsen, "Windows to FFT analysis (Part I)",
             Technical Review 3, Bruel & Kjaer, 1987.
  
      Examples
      --------
      Plot the symmetric window and its frequency response:
  
      >>> from scipy import signal
      >>> from scipy.fft import fft, fftshift
      >>> import matplotlib.pyplot as plt
  
      >>> M = 51
      >>> tau = 3.0
      >>> window = signal.windows.exponential(M, tau=tau)
      >>> plt.plot(window)
      >>> plt.title("Exponential Window (tau=3.0)")
      >>> 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, -35, 0])
      >>> plt.title("Frequency response of the Exponential window (tau=3.0)")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")
  
      This function can also generate non-symmetric windows:
  
      >>> tau2 = -(M-1) / np.log(0.01)
      >>> window2 = signal.windows.exponential(M, 0, tau2, False)
      >>> plt.figure()
      >>> plt.plot(window2)
      >>> plt.ylabel("Amplitude")
      >>> plt.xlabel("Sample")
      """
      if sym and center is not None:
          raise ValueError("If sym==True, center must be None.")
      if _len_guards(M):
          return np.ones(M)
      M, needs_trunc = _extend(M, sym)
  
      if center is None:
          center = (M - 1) / 2
  
      n = np.arange(0, M)
      w = np.exp(-np.abs(n - center) / tau)
  
      return _truncate(w, needs_trunc)
  
imports: import operator
  import warnings
  import numpy
  from scipy import linalg, special, fft
label_desc: Use image node_id 25 for calling a global function with example usage: exponential(M, center, tau, sym) and returns: _truncate, np