scipy.signal.exponential¶

scipy.signal.exponential(M, center=None, tau=1.0, sym=True)[source]

Return an exponential (or Poisson) window.

Parameters: M : int Number of points in the output window. If zero or less, an empty array is returned. center : float, optional Parameter defining the center location of the window function. The default value if not given is center = (M-1) / 2. This parameter must take its default value for symmetric windows. tau : float, optional Parameter defining the decay. For center = 0 use tau = -(M-1) / ln(x) if x is the fraction of the window remaining at the end. 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. 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 Exponential window is defined as

$w(n) = e^{-|n-center| / \tau}$

References

S. Gade and H. Herlufsen, “Windows to FFT analysis (Part I)”, Technical Review 3, Bruel & Kjaer, 1987.

Examples

Plot the symmetric window and its frequency response:

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

>>> M = 51
>>> tau = 3.0
>>> window = signal.exponential(M, tau=tau)
>>> plt.plot(window)
>>> plt.title("Exponential Window (tau=3.0)")
>>> 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, -35, 0])
>>> plt.title("Frequency response of the Exponential window (tau=3.0)")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")


This function can also generate non-symmetric windows:

>>> tau2 = -(M-1) / np.log(0.01)
>>> window2 = signal.exponential(M, 0, tau2, False)
>>> plt.figure()
>>> plt.plot(window2)
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")   Previous topic

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