scipy.signal.windows.

gaussian#

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

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]")
../../_images/scipy-signal-windows-gaussian-1_00.png
../../_images/scipy-signal-windows-gaussian-1_01.png