cupyx.scipy.signal.windows.gaussian#
- cupyx.scipy.signal.windows.gaussian(M, std, sym=True)[source]#
Return a Gaussian window.
- Parameters:
M (int) – Number of points in the output window. If zero or less, an empty array is returned.
std (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:
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 cupyx.scipy.signal.windows >>> import cupy as cp >>> from cupy.fft import fft, fftshift >>> import matplotlib.pyplot as plt
>>> window = cupyx.scipy.signal.windows.gaussian(51, std=7) >>> plt.plot(cupy.asnumpy(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 = 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"Frequency response of the Gaussian window ($\sigma$=7)") >>> plt.ylabel("Normalized magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]")