bartlett

→Tensor

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

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Bartlett (triangular) window.

Generates a triangular taper that ramps linearly from 0 to 1 and back to 0 across the window length. Equivalent to the convolution of two boxcar windows, the Bartlett window provides the simplest non-trivial reduction of spectral leakage at the price of a wider main lobe.

Parameters

Mint

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

symbool= True

If True (default) generate a symmetric window suitable for filter design. If False generate a periodic window suitable for use with the DFT (the length-

M+1

symmetric form with the last sample dropped).

dtypeDTypeLike= None

Desired dtype of the output tensor; defaults to float32.

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] = 1 - \left| \frac{2n}{N - 1} - 1 \right|, \qquad 0 \le n < N,

where $N = M$ (symmetric) or $N = M + 1$ (periodic). The main-lobe width is roughly $8\pi / N$ (about twice that of the rectangular window) and the peak side-lobe attenuation is $\approx -26.5\, \text{dB}$ .

Examples

>>> from lucid.signal.windows import bartlett
>>> bartlett(5)
Tensor([0.0000, 0.5000, 1.0000, 0.5000, 0.0000])