# cupyx.scipy.signal.windows.exponential#

cupyx.scipy.signal.windows.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.

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 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:

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

>>> M = 51
>>> tau = 3.0
>>> window = cupyx.scipy.signal.windows.exponential(M, tau=tau)
>>> plt.plot(cupy.asnumpy(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 = 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, -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 = cupyx.scipy.signal.windows.exponential(M, 0, tau2, False)
>>> plt.figure()
>>> plt.plot(cupy.asnumpy(window2))
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")