scipy.signal.windows.gaussian

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

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.

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

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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]")

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