hfft2

→Tensor

hfft2(input: Tensor, s: Sequence[int] | None = None, dim: Sequence[int] = (-2, -1), norm: str | None = None)

source

2-D FFT of a Hermitian-symmetric complex signal over a pair of axes.

Computes the two-dimensional DFT of a Hermitian signal stored as a one-sided half-spectrum (as produced by ihfft2), returning a real-valued output. This is the 2-D specialisation of hfftn.

For an input of shape $(M, m)$ where $m = N//2 + 1$ , the output shape is $(M, N)$ .

Parameters

inputTensor

Complex Hermitian half-spectrum tensor with at least 2 dimensions.

ssequence of int= None

Full output sizes (M_out, N_out) along the two transformed axes. If None, the last axis defaults to

2(m-1)

dimsequence of int= (-2, -1)

The two axes over which to compute the transform. Default is (-2, -1).

normstr or None= None

Normalisation mode — "backward" (default), "forward", or "ortho". See fftn for the full description.

Returns

Tensor

Real tensor (float32) with the same shape as input except the last transformed axis has length s[-1] (or $2(m-1)$ by default).

Notes

Odd-length last axis — always pass s explicitly when the original last axis had an odd length to avoid the default $2(m-1)$ even-length assumption.

Examples

Recover a real 2-D signal from its Hermitian half-spectrum:
>>> H = lucid.randn(64, 33)   # half-spectrum for 64×64 real image
>>> y = lucid.fft.hfft2(H, s=[64, 64])
>>> y.shape
(64, 64)