large, the window narrows, and so the number of samples needs to be
large enough to sample the increasingly narrow spike, otherwise NaNs will
get 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

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> np.kaiser(12, 14)
 array([7.72686684e-06, 3.46009194e-03, 4.65200189e-02, # may vary
        2.29737120e-01, 5.99885316e-01, 9.45674898e-01,
        9.45674898e-01, 5.99885316e-01, 2.29737120e-01,
        4.65200189e-02, 3.46009194e-03, 7.72686684e-06])


Plot the window and the frequency response.

.. plot::
    :include-source:

    import matplotlib.pyplot as plt
    from numpy.fft import fft, fftshift
    window = np.kaiser(51, 14)
    plt.plot(window)
    plt.title("Kaiser window")
    plt.ylabel("Amplitude")
    plt.xlabel("Sample")
    plt.show()

    plt.figure()
    A = fft(window, 2048) / 25.5
    mag = np.abs(fftshift(A))
    freq = np.linspace(-0.5, 0.5, len(A))
    response = 20 * np.log10(mag)
    response = np.clip(response, -100, 100)
    plt.plot(freq, response)
    plt.title("Frequency response of Kaiser window")
    plt.ylabel("Magnitude [dB]")
    plt.xlabel("Normalized frequency [cycles per sample]")
    plt.axis('tight')
    plt.show()

r‘