blackman

→Tensor

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

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Blackman window.

Three-term cosine-sum window designed by Blackman and Tukey to drive the first three side-lobes substantially below the Hann level. Peak side-lobe attenuation is $\approx -58\, \text{dB}$ with a main-lobe roughly twice as wide as the Hann window.

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 (special case of general_cosine with coefficients [0.42, 0.50, 0.08]):

w[n] = 0.42 - 0.50 \cos\!\left(\frac{2\pi n}{N - 1}\right) + 0.08 \cos\!\left(\frac{4\pi n}{N - 1}\right), \qquad 0 \le n < N.

The slightly different "exact Blackman" uses coefficients derived from the first two zeros of the side-lobe envelope; the standard [0.42, 0.50, 0.08] truncation used here is the textbook form.

Examples

>>> import lucid
>>> from lucid.signal.windows import blackman
>>> w = blackman(5)  # the endpoints are zero up to float32 round-off
>>> lucid.allclose(w, lucid.tensor([0.0, 0.34, 1.0, 0.34, 0.0]), atol=1e-6)
True

Used by 1

lucid._ops.composite.spectral

>>> import lucid >>> from lucid.signal.windows import blackman >>> w = blackman(5) # the endpoints are zero up to float32 round-off >>> lucid.allclose(w, lucid.tensor([0.0, 0.34, 1.0, 0.34, 0.0]), atol=1e-6) True