# tensorplay.signal.windows.nuttall

Source: https://www.tensorplay.cn/docs/generated/tensorplay.signal.windows.nuttall.html

```python
tensorplay.signal.windows.nuttall(M: int, *, sym: bool = True, dtype: dtype | None = None, layout: Layout = tensorplay.strided, device: device | None = None, requires_grad: bool = False) → Tensor
```

Computes the minimum 4-term Blackman-Harris window described by Nuttall.

The window is a general cosine sum with the Nuttall coefficients
$a_0 = 0.3635819$, $a_1 = 0.4891775$, $a_2 = 0.1365995$,
$a_3 = 0.0106411$:

$$w_n = a_0 - a_1 \cos{(z_n)} + a_2 \cos{(2z_n)} - a_3 \cos{(3z_n)}$$

where $z_n = \frac{2 \pi n}{M - 1}$ for a symmetric window and
$z_n = \frac{2 \pi n}{M}$ for a periodic one.

The window is scaled so that its largest value is 1. The value 1 itself does not occur when M is even and sym is True.

Parameters:

M ([int](https://docs.python.org/3/builtins/functions.html#int)) – number of points of the returned window.

Keyword Arguments:

- sym ([bool](https://docs.python.org/3/builtins/functions.html#bool), optional) – if False, returns a periodic window, which is the usual choice for spectral analysis. If True, returns a symmetric window, which is the usual choice for filter design. Default: True.

- dtype ([tensorplay.dtype](/docs/generated/tensorplay.DType.html#tensorplay.DType), optional) – the desired data type of the returned tensor. Default: if None, uses the global default (see [tensorplay.set_default_dtype()](/docs/generated/tensorplay.set_default_dtype.html#tensorplay.set_default_dtype)).

- layout ([tensorplay.Layout](/docs/generated/tensorplay.Layout.html#tensorplay.Layout), optional) – the desired layout of the returned tensor. Default: tensorplay.strided.

- device ([tensorplay.device](/docs/generated/tensorplay.Device.html#tensorplay.Device), optional) – the desired device of the returned tensor. Default: if None, uses the current default tensor device (see [tensorplay.set_default_device()](/docs/generated/tensorplay.set_default_device.html#tensorplay.set_default_device)).

- requires_grad ([bool](https://docs.python.org/3/builtins/functions.html#bool), optional) – whether autograd should record operations on the returned tensor. Default: False.

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:

```
>>> # Symmetric Nuttall window.
>>> tensorplay.signal.windows.nuttall(5)
tensor([0.0004, 0.227, 1., 0.227, 0.0004])

>>> # Periodic Nuttall window.
>>> tensorplay.signal.windows.nuttall(5, sym=False)
tensor([0.0004, 0.1105, 0.7983, 0.7983, 0.1105])
```