code: def kaiser(M, beta, sym=True):
      r"""Return a Kaiser window.
  
      The Kaiser window is a taper formed by using a Bessel function.
  
      Parameters
      ----------
      M : int
          Number of points in the output window. If zero or less, an empty
          array is returned.
      beta : float
          Shape parameter, determines trade-off between main-lobe width and
          side lobe level. As beta gets large, the window narrows.
      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 Kaiser window is defined as
  
      .. math::  w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}}
                 \right)/I_0(\beta)
  
      with
  
      .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2},
  
      where :math:`I_0` is the modified zeroth-order Bessel function.
  
      The Kaiser was named for Jim Kaiser, who discovered a simple approximation
      to the DPSS window based on Bessel functions.
      The Kaiser window is a very good approximation to the Digital Prolate
      Spheroidal Sequence, or Slepian window, which is the transform which
      maximizes the energy in the main lobe of the window relative to total
      energy.
  
      The Kaiser can approximate other windows by varying the beta parameter.
      (Some literature uses alpha = beta/pi.) [4]_
  
      ====  =======================
      beta  Window shape
      ====  =======================
      0     Rectangular
      5     Similar to a Hamming
      6     Similar to a Hann
      8.6   Similar to a Blackman
      ====  =======================
  
      A beta value of 14 is probably a good starting point. Note that as beta
      gets large, the window narrows, and so the number of samples needs to be
      large enough to sample the increasingly narrow spike, otherwise NaNs will
      be returned.
  
      Most references to the Kaiser window come from the signal processing
      literature, where it is used as one of many windowing functions for
      smoothing values.  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.
  
      References
      ----------
      .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by
             digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285.
             John Wiley and Sons, New York, (1966).
      .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
             University of Alberta Press, 1975, pp. 177-178.
      .. [3] Wikipedia, "Window function",
             https://en.wikipedia.org/wiki/Window_function
      .. [4] F. J. Harris, "On the use of windows for harmonic analysis with the
             discrete Fourier transform," Proceedings of the IEEE, vol. 66,
             no. 1, pp. 51-83, Jan. 1978. :doi:`10.1109/PROC.1978.10837`.
  
      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.kaiser(51, beta=14)
      >>> plt.plot(window)
      >>> plt.title(r"Kaiser window ($\beta$=14)")
      >>> 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(r"Frequency response of the Kaiser window ($\beta$=14)")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")
  
      """
      # Docstring adapted from NumPy's kaiser function
      if _len_guards(M):
          return np.ones(M)
      M, needs_trunc = _extend(M, sym)
  
      n = np.arange(0, M)
      alpha = (M - 1) / 2.0
      w = special.i0(
          beta * np.sqrt(1 - ((n - alpha) / alpha) ** 2.0)
      ) / special.i0(beta)
  
      return _truncate(w, needs_trunc)
  
imports: from __future__ import division, print_function, absolute_import
  import operator
  import warnings
  import numpy
  from scipy import fftpack, linalg, special
  from scipy._lib.six import string_types
label_desc: Use image node_id 20 for calling a global function with example usage: kaiser(M, beta, sym) and returns: _truncate, np