scipy.signal.slepian(M, width, sym=True)[source]

Return a digital Slepian (DPSS) window.

Used to maximize the energy concentration in the main lobe. Also called the digital prolate spheroidal sequence (DPSS).


M : int

Number of points in the output window. If zero or less, an empty array is returned.

width : float


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 always normalized to 1


[R298]D. Slepian & H. O. Pollak: “Prolate spheroidal wave functions, Fourier analysis and uncertainty-I,” Bell Syst. Tech. J., vol.40, pp.43-63, 1961.
[R299]H. J. Landau & H. O. Pollak: “Prolate spheroidal wave functions, Fourier analysis and uncertainty-II,” Bell Syst. Tech. J. , vol.40, pp.65-83, 1961.


Plot the window and its frequency response:

>>> from scipy import signal
>>> from scipy.fftpack import fft, fftshift
>>> import matplotlib.pyplot as plt
>>> window = signal.slepian(51, width=0.3)
>>> plt.plot(window)
>>> plt.title("Slepian (DPSS) window (BW=0.3)")
>>> 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, -120, 0])
>>> plt.title("Frequency response of the Slepian window (BW=0.3)")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")

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