scipy.signal.general_gaussian

scipy.signal.general_gaussian(M, p, sig, sym=True)

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 : ndarray

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 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:

>>> from scipy import signal
>>> from scipy.fftpack import fft, fftshift
>>> import matplotlib.pyplot as plt

>>> window = signal.general_gaussian(51, 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 "
...           "window (p=1.5, $\sigma$=7)")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")