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# torch.signal.windows.nuttall

torch.signal.windows.nuttall(M, *, sym=True, dtype=None, layout=torch.strided, device=None, requires_grad=False)

  Computes the minimum 4-term Blackman-Harris window according to Nuttall.

  w n=1−0.36358 cos⁡(z n)+0.48917 cos⁡(2 z n)−0.13659 cos⁡(3 z n)+0.01064 cos⁡(4 z n)w_n = 1 - 0.36358 \cos{(z_n)} + 0.48917 \cos{(2z_n)} - 0.13659 \cos{(3z_n)} + 0.01064 \cos{(4z_n)} w n​=1−0.36358 cos(z n​)+0.48917 cos(2 z n​)−0.13659 cos(3 z n​)+0.01064 cos(4 z n​)

  where `z_n = 2 π n/ M`.

  The window is normalized to 1 (maximum value is 1). However, the 1 doesn’t appear if `M` is even and `sym` is True.

  Parameters:

    M (int) – the length of the window. In other words, the number of points of the returned window.

  Keyword Arguments:

    - sym (bool, optional) – If False, returns a periodic window suitable for use in spectral analysis. If True, returns a symmetric window suitable for use in filter design. Default: True.

    - dtype (`torch.dtype`, optional) – the desired data type of returned tensor. Default: if `None`, uses a global default (see `torch.set_default_tensor_type()`).

    - layout (`torch.layout`, optional) – the desired layout of returned Tensor. Default: `torch.strided`.

    - device (`torch.device`, optional) – the desired device of returned tensor. Default: if `None`, uses the current device for the default tensor type (see `torch.set_default_tensor_type()`). `device` will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.

    - requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: `False`.

  Return type:

    Tensor

  References:

      - 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. https://doi.org/10.1109/TASSP.1981.1163506

      - 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:

      >>> # Generates a symmetric Nutall window.
      >>> torch.signal.windows.general_hamming(5, sym=True)
      tensor([3.6280e-04, 2.2698e-01, 1.0000e+00, 2.2698e-01, 3.6280e-04])

      >>> # Generates a periodic Nuttall window.
      >>> torch.signal.windows.general_hamming(5, sym=False)
      tensor([3.6280e-04, 1.1052e-01, 7.9826e-01, 7.9826e-01, 1.1052e-01])

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