hann

→Tensor

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

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Hann (raised-cosine) window.

The Hann window is a single full cycle of a raised cosine. Its side-lobes roll off at $-18\,\text{dB/octave}$ , the fastest asymptotic decay among the simple cosine-sum windows, which makes it a popular default for STFT analysis when temporal localisation matters more than peak side-lobe suppression.

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 containing the window samples.

Notes

Sample formula (special case of general_hamming with $\alpha = 0.5$ ):

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

Main-lobe width $8\pi/N$ , peak side-lobe attenuation $-31.5\,\text{dB}$ . Vanishes at both endpoints.

Examples

>>> import lucid
>>> from lucid.signal.windows import hann
>>> w = hann(5)  # the endpoints are zero up to float32 round-off
>>> lucid.allclose(w, lucid.tensor([0.0, 0.5, 1.0, 0.5, 0.0]), atol=1e-6)
True

Used by 1

lucid._ops.composite.spectral

>>> import lucid >>> from lucid.signal.windows import hann >>> w = hann(5) # the endpoints are zero up to float32 round-off >>> lucid.allclose(w, lucid.tensor([0.0, 0.5, 1.0, 0.5, 0.0]), atol=1e-6) True