# cupyx.scipy.signal.windows.general_gaussian#

cupyx.scipy.signal.windows.general_gaussian(M, p, sig, sym=True)[source]#

Return a window with a generalized Gaussian shape.

Parameters
• M (int) – Number of points in the output window. If zero or less, an empty array is returned.

• p (float) – Shape parameter. p = 1 is identical to gaussian, p = 0.5 is the same shape as the Laplace distribution.

• sig (float) – The standard deviation, sigma.

• sym (bool, 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

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

Return type

ndarray

Notes

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

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

Examples

Plot the window and its frequency response:

>>> import cupyx.scipy.signal.windows
>>> import cupy as cp
>>> from cupy.fft import fft, fftshift
>>> import matplotlib.pyplot as plt

>>> window = cupyx.scipy.signal.windows.general_gaussian(51, p=1.5, sig=7)
>>> plt.plot(cupy.asnumpy(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 = cupy.linspace(-0.5, 0.5, len(A))
>>> response = 20 * cupy.log10(cupy.abs(fftshift(A / cupy.abs(A).max())))
>>> plt.plot(cupy.asnumpy(freq), cupy.asnumpy(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]")