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exponential(M, center=None, tau=1.0, sym=True)

Notes

The Exponential window is defined as

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

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.

Returns

w : ndarray

The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and :None:None:`sym` is True).

Return an exponential (or Poisson) window.

Examples

Plot the symmetric window and its frequency response:

>>> from scipy import signal
... from scipy.fft import fft, fftshift
... import matplotlib.pyplot as plt
>>> M = 51
... tau = 3.0
... window = signal.windows.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.windows.exponential(M, 0, tau2, False)
... plt.figure()
... plt.plot(window2)
... plt.ylabel("Amplitude")
... plt.xlabel("Sample")
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal.windows._windows.exponential scipy.signal.windows._windows.get_window scipy.signal.exponential

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GitHub : /scipy/signal/windows/_windows.py#1535
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