parameters: (M, width, sym=True)
return_statement: return _truncate(win, needs_trunc)
docstring: Return a digital Slepian (DPSS) window.
  
      Used to maximize the energy concentration in the main lobe.  Also called
      the digital prolate spheroidal sequence (DPSS).
  
      Parameters
      ----------
      M : int
          Number of points in the output window. If zero or less, an empty
          array is returned.
      width : float
          Bandwidth
      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 always normalized to 1
  
      References
      ----------
      .. [1] D. Slepian & H. O. Pollak: "Prolate spheroidal wave functions,
             Fourier analysis and uncertainty-I," Bell Syst. Tech. J., vol.40,
             pp.43-63, 1961. https://archive.org/details/bstj40-1-43
      .. [2] 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. https://archive.org/details/bstj40-1-65
  
      Examples
      --------
      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]")
docstring_summary: Return a digital Slepian (DPSS) window.
docstring_tokens: Return a digital Slepian ( DPSS ) window .
function: def slepian(M, width, sym=True):
      """Return a digital Slepian (DPSS) window.
  
      Used to maximize the energy concentration in the main lobe.  Also called
      the digital prolate spheroidal sequence (DPSS).
  
      Parameters
      ----------
      M : int
          Number of points in the output window. If zero or less, an empty
          array is returned.
      width : float
          Bandwidth
      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 always normalized to 1
  
      References
      ----------
      .. [1] D. Slepian & H. O. Pollak: "Prolate spheroidal wave functions,
             Fourier analysis and uncertainty-I," Bell Syst. Tech. J., vol.40,
             pp.43-63, 1961. https://archive.org/details/bstj40-1-43
      .. [2] 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. https://archive.org/details/bstj40-1-65
  
      Examples
      --------
      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]")
  
      """
      if _len_guards(M):
          return np.ones(M)
      M, needs_trunc = _extend(M, sym)
  
      # our width is the full bandwidth
      width = width / 2
      # to match the old version
      width = width / 2
      m = np.arange(M, dtype='d')
      H = np.zeros((2, M))
      H[0, 1:] = m[1:] * (M - m[1:]) / 2
      H[1, :] = ((M - 1 - 2 * m) / 2)**2 * np.cos(2 * np.pi * width)
  
      _, win = linalg.eig_banded(H, select='i', select_range=(M-1, M-1))
      win = win.ravel() / win.max()
  
      return _truncate(win, needs_trunc)
function_tokens: def slepian ( M , width , sym = True ) : if _len_guards ( M ) : return np . ones ( M ) M , needs_trunc = _extend ( M , sym ) # our width is the full bandwidth width = width / 2 # to match the old version width = width / 2 m = np . arange ( M , dtype = 'd' ) H = np . zeros ( ( 2 , M ) ) H [ 0 , 1 : ] = m [ 1 : ] * ( M - m [ 1 : ] ) / 2 H [ 1 , : ] = ( ( M - 1 - 2 * m ) / 2 ) ** 2 * np . cos ( 2 * np . pi * width ) _ , win = linalg . eig_banded ( H , select = 'i' , select_range = ( M - 1 , M - 1 ) ) win = win . ravel ( ) / win . max ( ) return _truncate ( win , needs_trunc )