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# scipy.signal.windows.general_gaussian

scipy.signal.windows.general_gaussian(M, p, sig, sym=True)

  Return a window with a generalized Gaussian shape.

  Parameters:
    M int

      Number of points in the output window. If zero, an empty array is returned. An exception is thrown when it is negative.

    p float

      Shape parameter. p = 1 is identical to `gaussian`, p = 0.5 is the same shape as the Laplace distribution.

    sig float

      The standard deviation, sigma.

    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 generalized Gaussian window is defined as

  \[w(n) = e^{ -\frac{1}{2}\left|\frac{n}{\sigma}\right|^{2p} }\]

  the half-power point is at

  \[(2 \log(2))^{1/(2 p)} \sigma\]

  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.general_gaussian(51, p=1.5, sig=7)
      >>> plt.plot(window)
      >>> plt.title(r"Generalized Gaussian window (p=1.5, $\sigma$=7)")
      >>> 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"Freq. resp. of the gen. Gaussian "
      ...           r"window (p=1.5, $\sigma$=7)")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")