Skip to main content
`Ctrl`+`K`
scipy.signal.windows.

# gaussian

scipy.signal.windows.gaussian(M, std, sym=True, *, xp=None, device=None)

  Return a Gaussian window.

  Parameters:
    Mint

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

    stdfloat

      The standard deviation, sigma.

    symbool, optional

      When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis.

    xparray_namespace, optional

      Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: `numpy`

    device: any

      optional device specification for output. Should match one of the supported device specification in `xp`.

  Returns:
    wndarray

      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 Gaussian window is defined as

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

  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.gaussian(51, std=7)
      >>> plt.plot(window)
      >>> plt.title(r"Gaussian window ($\sigma$=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"Frequency response of the Gaussian window ($\sigma$=7)")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")