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# scipy.signal.tukey

`scipy.signal.``tukey`(M, alpha=0.5, sym=True)

  Return a Tukey window, also known as a tapered cosine window.

  Parameters: | M : int Number of points in the output window. If zero or less, an empty array is returned. alpha : float, optional Shape parameter of the Tukey window, representing the faction of the window inside the cosine tapered region. If zero, the Tukey window is equivalent to a rectangular window. If one, the Tukey window is equivalent to a Hann window. 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).

  References

  [R198] | Harris, Fredric J. (Jan 1978). “On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform”. Proceedings of the IEEE 66 (1): 51-83. doi:10.1109/PROC.1978.10837

  [R199] | Wikipedia, “Window function”, http://en.wikipedia.org/wiki/Window_function#Tukey_window

  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.tukey(51)
      >>> plt.plot(window)
      >>> plt.title("Tukey window")
      >>> plt.ylabel("Amplitude")
      >>> plt.xlabel("Sample")
      >>> plt.ylim([0, 1.1])

      >>> 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 Tukey window")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")

  (Source code)