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# torch.signal.windows.kaiser

torch.signal.windows.kaiser(M, *, beta=12.0, sym=True, dtype=None, layout=torch.strided, device=None, requires_grad=False)

  Computes the Kaiser window.

  The Kaiser window is defined as follows:

  w n=I 0(β 1−(n−N/2 N/2)2)/I 0(β)w_n = I_0 \left( \beta \sqrt{1 - \left( {\frac{n - N/2}{N/2}} \right) ^2 } \right) / I_0( \beta ) w n​=I 0​
  ​β 1−(N/2 n−N/2​)2
  ​
  ​/I 0​(β)

  where `I_0` is the zeroth order modified Bessel function of the first kind (see `torch.special.i0()`), and `N = M - 1 if sym else 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:

    - beta (float, optional) – shape parameter for the window. Must be non-negative. Default: 12.0

    - 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

  Examples:

      >>> # Generates a symmetric gaussian window with a standard deviation of 1.0.
      >>> torch.signal.windows.kaiser(5)
      tensor([4.0065e-05, 2.1875e-03, 4.3937e-02, 3.2465e-01, 8.8250e-01, 8.8250e-01, 3.2465e-01, 4.3937e-02, 2.1875e-03, 4.0065e-05])
      >>> # Generates a periodic gaussian window and standard deviation equal to 0.9.
      >>> torch.signal.windows.kaiser(5, sym=False,std=0.9)
      tensor([1.9858e-07, 5.1365e-05, 3.8659e-03, 8.4658e-02, 5.3941e-01, 1.0000e+00, 5.3941e-01, 8.4658e-02, 3.8659e-03, 5.1365e-05])

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