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.

$$w_n = 1 - 0.36358 \cos{(z_n)} + 0.48917 \cos{(2z_n)} - 0.13659 \cos{(3z_n)} + 0.01064 \cos{(4z_n)}$$

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])