irfft2

→Tensor

irfft2(input: Tensor, s: Sequence[int] | None = None, dim: Sequence[int] = (-2, -1), norm: str | None = None)

source

2-D inverse FFT for a Hermitian-symmetric spectrum.

Recovers a real 2-D signal from its one-sided 2-D spectrum as produced by rfft2. The output is guaranteed to be real-valued.

For an input of shape $(M, m)$ where $m = \lfloor N/2 \rfloor + 1$ , the default full output size is $(M, 2(m-1))$ (assuming an even last-axis length $N$ ).

Parameters

inputTensor

Complex Hermitian tensor (one-sided 2-D spectrum) with at least 2 dimensions, typically the output of rfft2.

ssequence of int= None

Full output sizes (M_out, N_out) along the two transformed axes. Pass the original signal shape to avoid the even/odd ambiguity in the last axis. If None, the last axis defaults to

2(m-1)

dimsequence of int= (-2, -1)

The two axes over which to compute the inverse 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 two transformed axes have lengths s[0] and s[1] (or inferred sizes when s is None).

Notes

Odd-length last axis — if the original image had an odd number of columns $N$ , always pass s=[M, N] explicitly.

Examples

Round-trip for a 128×256 image:
>>> x = lucid.randn(128, 256)
>>> X = lucid.fft.rfft2(x)
>>> X.shape   # (128, 129)
(128, 129)
>>> x_rec = lucid.fft.irfft2(X, s=[128, 256])
>>> x_rec.shape
(128, 256)