antenna arrays.

Unlike most windows, the Dolph-Chebyshev is defined in terms of its
frequency response:

.. math:: W(k) = \frac
          {\cos\{M \cos^{-1}[\beta \cos(\frac{\pi k}{M})]\}}
          {\cosh[M \cosh^{-1}(\beta)]}

where

.. math:: \beta = \cosh \left [\frac{1}{M}
          \cosh^{-1}(10^\frac{A}{20}) \right ]

and 0 <= abs(k) <= M-1. A is the attenuation in decibels (`at`).

The time domain window is then generated using the IFFT, so
power-of-two `M` are the fastest to generate, and prime number `M` are
the slowest.

The equiripple condition in the frequency domain creates impulses in the
time domain, which appear at the ends of the window.

References
----------
.. [1] C. Dolph, "A current distribution for broadside arrays which
       optimizes the relationship between beam width and side-lobe level",
       Proceedings of the IEEE, Vol. 34, Issue 6
.. [2] Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal Filter",
       American Meteorological Society (April 1997)
       http://mathsci.ucd.ie/~plynch/Publications/Dolph.pdf
.. [3] F. J. Harris, "On the use of windows for harmonic analysis with the
       discrete Fourier transforms", Proceedings of the IEEE, Vol. 66,
       No. 1, January 1978

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.chebwin(51, at=100)
>>> plt.plot(window)
>>> plt.title("Dolph-Chebyshev window (100 dB)")
>>> 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("Frequency response of the Dolph-Chebyshev window (100 dB)")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")

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