nuttall

→Tensor

nuttall(M: int, sym: bool = True, dtype: DTypeLike = None, device: DeviceLike = None)

source

Nuttall four-term window.

A four-term cosine-sum window with coefficients optimised by Nuttall to drive the peak side-lobe to approximately $-98\, \text{dB}$ , the deepest practical suppression among four-term windows. Useful for very-high-dynamic-range spectral analysis at the cost of a wider main lobe.

Parameters

Mint

Number of samples in the output window; must be >= 0.

symbool= True

Symmetric (True, default) or periodic (False) variant.

dtypeDTypeLike= None

Desired dtype of the output tensor.

deviceDeviceLike= None

Target device for the output tensor.

Returns

Tensor

1-D tensor of length M.

Notes

Sample formula (four-term general_cosine with coefficients [0.3635819, 0.4891775, 0.1365995, 0.0106411]):

w[n] = 0.3635819 - 0.4891775 \cos\!\left(\frac{2\pi n}{N - 1}\right) + 0.1365995 \cos\!\left(\frac{4\pi n}{N - 1}\right) - 0.0106411 \cos\!\left(\frac{6\pi n}{N - 1}\right).

The main-lobe is roughly $16\pi/N$ wide.

Examples

>>> from lucid.signal.windows import nuttall
>>> nuttall(5)
Tensor([0.0004, 0.2270, 1.0000, 0.2270, 0.0004])