cosine

→Tensor

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

source

Cosine (half-sine) window.

Produces a single arch of a sine curve over the window length, sometimes called the "sine" or "half-cosine" window. It is a smoother taper than the triangular window with comparable main-lobe width but significantly lower side lobes.

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:

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

Peak side-lobe attenuation is $\approx -23\, \text{dB}$ and the main-lobe width is $4\pi/N$ . Sometimes used as the square root of the Hann window for analysis/synthesis pairs.

Examples

>>> from lucid.signal.windows import cosine
>>> cosine(4)
Tensor([0.3827, 0.9239, 0.9239, 0.3827])