# tensorplay.signal.windows.kaiser

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

```python
tensorplay.signal.windows.kaiser(M: int, *, beta: float = 12.0, sym: bool = True, dtype: dtype | None = None, layout: Layout = tensorplay.strided, device: device | None = None, requires_grad: bool = False) → Tensor
```

Computes the Kaiser window.

The samples are

$$w_n = I_0 \left( \beta \sqrt{1 - \left( {\frac{n - N/2}{N/2}} \right) ^2 } \right) / I_0( \beta )$$

where $I_0$ is the modified Bessel function of the first kind of order
zero, evaluated with tensorplay.i0(), and $N = M - 1$ for a
symmetric window, otherwise $N = M$.

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:

- beta ([float](https://docs.python.org/3/builtins/functions.html#float), optional) – shape parameter of the window. Must be non-negative. Default: 12.0

- 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.

Examples:

```
>>> # Symmetric Kaiser window of length 5 with shape parameter 12.0.
>>> tensorplay.signal.windows.kaiser(5)
tensor([0.0001, 0.2157, 1., 0.2157, 0.0001])

>>> # Periodic Kaiser window of length 5 with shape parameter 0.9.
>>> tensorplay.signal.windows.kaiser(5, sym=False, beta=0.9)
tensor([0.8244, 0.9348, 0.9926, 0.9926, 0.9348])
```