chebwin(M, at, sym=True)
This window optimizes for the narrowest main lobe width for a given order M and sidelobe equiripple attenuation :None:None:`at`, using Chebyshev polynomials. It was originally developed by Dolph to optimize the directionality of radio antenna arrays.
Unlike most windows, the Dolph-Chebyshev is defined in terms of its frequency response:
$$W(k) = \frac{\cos\{M \cos^{-1}[\beta \cos(\frac{\pi k}{M})]\}} {\cosh[M \cosh^{-1}(\beta)]}$$where
$$\beta = \cosh \left [\frac{1}{M}\cosh^{-1}(10^\frac{A}{20}) \right ]$$and 0 <= abs(k) <= M-1. A is the attenuation in decibels (:None:None:`at`).
The time domain window is then generated using the IFFT, so power-of-two M are the fastest to generate, and prime number M are the slowest.
The equiripple condition in the frequency domain creates impulses in the time domain, which appear at the ends of the window.
Number of points in the output window. If zero or less, an empty array is returned.
Attenuation (in dB).
When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis.
The window, with the maximum value always normalized to 1
Return a Dolph-Chebyshev window.
Plot the window and its frequency response:
>>> from scipy import signal
... from scipy.fft import fft, fftshift
... import matplotlib.pyplot as plt
>>> window = signal.windows.chebwin(51, at=100)
... plt.plot(window)
... plt.title("Dolph-Chebyshev window (100 dB)")
... plt.ylabel("Amplitude")
... plt.xlabel("Sample")
>>> plt.figure()See :
... 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("Frequency response of the Dolph-Chebyshev window (100 dB)")
... plt.ylabel("Normalized magnitude [dB]")
... plt.xlabel("Normalized frequency [cycles per sample]")
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal.windows._windows.chebwin
scipy.signal.windows._windows.get_window
scipy.signal.chebwin
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