general_gaussian#, p, sig, sym=True)[source]#

Return a window with a generalized Gaussian shape.


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


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


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.


The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and sym is True).


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

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


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 =, 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]")