ction.

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 discrete 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:

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

>>> window = signal.windows.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]")

r