# scipy.signal.windows.gaussian¶

scipy.signal.windows.gaussian(M, std, sym=True)[source]

Return a Gaussian window.

Parameters
Mint

Number of points in the output window. If zero or less, an empty array is returned.

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.

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:

>>> from scipy import signal
>>> from scipy.fft import fft, fftshift
>>> import matplotlib.pyplot as plt
>>> window = signal.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]")