exponential#
- scipy.signal.windows.exponential(M, center=None, tau=1.0, sym=True, *, xp=None, device=None)[source]#
- Return an exponential (or Poisson) window. - Parameters:
- Mint
- Number of points in the output window. If zero, an empty array is returned. An exception is thrown when it is negative. 
- centerfloat, 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.
- taufloat, optional
- Parameter defining the decay. For - center = 0use- tau = -(M-1) / ln(x)if- xis the fraction of the window remaining at the end.
- symbool, optional
- When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis. 
- xparray_namespace, optional
- Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: - numpy
- device: any
- optional device specification for output. Should match one of the supported device specification in - xp.
 
- Returns:
- wndarray
- 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 [1]- 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 numpy as np >>> 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")     