bartorch.fwt

bartorch.fwt()

Forward multi-level discrete wavelet transform along axes.

BART’s wavelet, or cdf97 for "cdf97".

Parameters:

• input (torch.Tensor) – Array to transform; every transformed axis has at least 16 samples.

• axes (int or tuple of int) – Axes to transform, as indices into input.shape.

• wavelet ({"haar", "dau2", "cdf44", "cdf97"}, default='dau2') – Haar, Daubechies with two vanishing moments, or CDF 4/4 and 9/7 biorthogonal; see Notes.

Returns:

For "cdf97", the shape of input. Otherwise the coefficients of all transformed axes are flattened into the last of axes, and the other transformed axes have size one.

Return type:

torch.Tensor

Raises:

ValueError – If wavelet is unknown, axes repeat or are out of range, or a transformed axis is shorter than 16.

Notes

"haar", "dau2" and "cdf44" are, along one axis, PyWavelets’ wavedec with "haar", "db2" and "bior4.4" in mode="symmetric", concatenated coarse first. Each level keeps (n + taps - 1) // 2 coefficients per band, so there are more coefficients than samples unless the filter has two taps and every level’s length is even; levels continue while that half-length is at least 16.

"cdf97" is CDF 9/7 by lifting, in place, coarse band first, with levels continuing while every transformed axis is longer than 32; one level of an even length is PyWavelets’ "bior4.4" in mode="periodization" with the detail band negated.