parameters: (M, a, sym=True)
return_statement: return _truncate(w, needs_trunc)
docstring: r"""
      Generic weighted sum of cosine terms window
  
      Parameters
      ----------
      M : int
          Number of points in the output window
      a : array_like
          Sequence of weighting coefficients. This uses the convention of being
          centered on the origin, so these will typically all be positive
          numbers, not alternating sign.
      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.
  
      References
      ----------
      .. [1] A. Nuttall, "Some windows with very good sidelobe behavior," IEEE
             Transactions on Acoustics, Speech, and Signal Processing, vol. 29,
             no. 1, pp. 84-91, Feb 1981. :doi:`10.1109/TASSP.1981.1163506`.
      .. [2] Heinzel G. et al., "Spectrum and spectral density estimation by the
             Discrete Fourier transform (DFT), including a comprehensive list of
             window functions and some new flat-top windows", February 15, 2002
             https://holometer.fnal.gov/GH_FFT.pdf
  
      Examples
      --------
      Heinzel describes a flat-top window named "HFT90D" with formula: [2]_
  
      .. math::  w_j = 1 - 1.942604 \cos(z) + 1.340318 \cos(2z)
                 - 0.440811 \cos(3z) + 0.043097 \cos(4z)
  
      where
  
      .. math::  z = \frac{2 \pi j}{N}, j = 0...N - 1
  
      Since this uses the convention of starting at the origin, to reproduce the
      window, we need to convert every other coefficient to a positive number:
  
      >>> HFT90D = [1, 1.942604, 1.340318, 0.440811, 0.043097]
  
      The paper states that the highest sidelobe is at -90.2 dB.  Reproduce
      Figure 42 by plotting the window and its frequency response, and confirm
      the sidelobe level in red:
  
      >>> from scipy.signal.windows import general_cosine
      >>> from scipy.fftpack import fft, fftshift
      >>> import matplotlib.pyplot as plt
  
      >>> window = general_cosine(1000, HFT90D, sym=False)
      >>> plt.plot(window)
      >>> plt.title("HFT90D window")
      >>> plt.ylabel("Amplitude")
      >>> plt.xlabel("Sample")
  
      >>> plt.figure()
      >>> A = fft(window, 10000) / (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([-50/1000, 50/1000, -140, 0])
      >>> plt.title("Frequency response of the HFT90D window")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")
      >>> plt.axhline(-90.2, color='red')
      >>> plt.show()
docstring_summary: r"""
      Generic weighted sum of cosine terms window
docstring_tokens: r Generic weighted sum of cosine terms window
function: def general_cosine(M, a, sym=True):
      r"""
      Generic weighted sum of cosine terms window
  
      Parameters
      ----------
      M : int
          Number of points in the output window
      a : array_like
          Sequence of weighting coefficients. This uses the convention of being
          centered on the origin, so these will typically all be positive
          numbers, not alternating sign.
      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.
  
      References
      ----------
      .. [1] A. Nuttall, "Some windows with very good sidelobe behavior," IEEE
             Transactions on Acoustics, Speech, and Signal Processing, vol. 29,
             no. 1, pp. 84-91, Feb 1981. :doi:`10.1109/TASSP.1981.1163506`.
      .. [2] Heinzel G. et al., "Spectrum and spectral density estimation by the
             Discrete Fourier transform (DFT), including a comprehensive list of
             window functions and some new flat-top windows", February 15, 2002
             https://holometer.fnal.gov/GH_FFT.pdf
  
      Examples
      --------
      Heinzel describes a flat-top window named "HFT90D" with formula: [2]_
  
      .. math::  w_j = 1 - 1.942604 \cos(z) + 1.340318 \cos(2z)
                 - 0.440811 \cos(3z) + 0.043097 \cos(4z)
  
      where
  
      .. math::  z = \frac{2 \pi j}{N}, j = 0...N - 1
  
      Since this uses the convention of starting at the origin, to reproduce the
      window, we need to convert every other coefficient to a positive number:
  
      >>> HFT90D = [1, 1.942604, 1.340318, 0.440811, 0.043097]
  
      The paper states that the highest sidelobe is at -90.2 dB.  Reproduce
      Figure 42 by plotting the window and its frequency response, and confirm
      the sidelobe level in red:
  
      >>> from scipy.signal.windows import general_cosine
      >>> from scipy.fftpack import fft, fftshift
      >>> import matplotlib.pyplot as plt
  
      >>> window = general_cosine(1000, HFT90D, sym=False)
      >>> plt.plot(window)
      >>> plt.title("HFT90D window")
      >>> plt.ylabel("Amplitude")
      >>> plt.xlabel("Sample")
  
      >>> plt.figure()
      >>> A = fft(window, 10000) / (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([-50/1000, 50/1000, -140, 0])
      >>> plt.title("Frequency response of the HFT90D window")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")
      >>> plt.axhline(-90.2, color='red')
      >>> plt.show()
      """
      if _len_guards(M):
          return np.ones(M)
      M, needs_trunc = _extend(M, sym)
  
      fac = np.linspace(-np.pi, np.pi, M)
      w = np.zeros(M)
      for k in range(len(a)):
          w += a[k] * np.cos(k * fac)
  
      return _truncate(w, needs_trunc)
function_tokens: def general_cosine ( M , a , sym = True ) : if _len_guards ( M ) : return np . ones ( M ) M , needs_trunc = _extend ( M , sym ) fac = np . linspace ( - np . pi , np . pi , M ) w = np . zeros ( M ) for k in range ( len ( a ) ) : w += a [ k ] * np . cos ( k * fac ) return _truncate ( w , needs_trunc )