general_hamming

→Tensor

general_hamming(M: int, alpha: float, sym: bool = True, dtype: DTypeLike = None, device: DeviceLike = None)

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Generalised Hamming-family window.

Parametric two-term cosine window covering the Hann ( $\alpha = 0.5$ ) / Hamming ( $\alpha = 0.54$ ) family. The free parameter $\alpha$ controls the trade-off between the level of the first side-lobe and the asymptotic side-lobe roll-off rate.

Parameters

Mint

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

alphafloat

Mixing coefficient;

\alpha = 0.5

gives Hann,

\alpha = 0.54

gives Hamming.

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 containing the window samples.

Notes

Sample formula:

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

With $\alpha = 25/46 \approx 0.5435$ the first side-lobe is minimised in absolute level (the so-called "optimal" Hamming).

Examples

>>> from lucid.signal.windows import general_hamming
>>> general_hamming(5, alpha=0.5)
Tensor([0.0000, 0.5000, 1.0000, 0.5000, 0.0000])