general_cosine

→Tensor

general_cosine(M: int, a: list[float] | tuple[float, ...], sym: bool = True, dtype: DTypeLike = None, device: DeviceLike = None)

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Generic weighted sum of cosines.

Builds a window of the form $\sum_k a_k (-1)^k \cos(2\pi k n / (N - 1))$ , the parent family from which Hann, Hamming, Blackman, Nuttall, and the flat-top window all derive. Allows custom coefficient designs for bespoke side-lobe characteristics.

Parameters

Mint

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

alist of float or tuple of float

Coefficients

a_0, a_1, \ldots

. The

k

-th coefficient multiplies

(-1)^k \cos(2\pi k n / (N - 1))

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:

w[n] = \sum_{k=0}^{K-1} (-1)^k a_k \cos\!\left( \frac{2\pi k n}{N - 1} \right), \qquad 0 \le n < N.

Common special cases:

Hann: [0.5, 0.5].
Hamming: [0.54, 0.46].
Blackman: [0.42, 0.50, 0.08].
Nuttall: [0.3635819, 0.4891775, 0.1365995, 0.0106411].

Examples

>>> from lucid.signal.windows import general_cosine
>>> general_cosine(5, [0.54, 0.46])  # Hamming, as a two-term cosine sum
tensor([0.08, 0.54, 1., 0.54, 0.08])

Used by 1

lucid._ops.composite.spectral