irfftn

→Tensor

irfftn(input: Tensor, s: int | Sequence[int] | None = None, dim: int | Sequence[int] | None = None, norm: str | None = None)

source

N-dimensional inverse FFT for a Hermitian-symmetric spectrum.

Computes the inverse N-dimensional FFT assuming the input is conjugate-symmetric (Hermitian), as produced by rfftn. The output is guaranteed to be real-valued.

For the last transformed axis, the full-length signal size must be specified or inferred: given an input last-axis of length $m = \lfloor N/2 \rfloor + 1$ , the default assumed full length is $N = 2(m - 1)$ (even). Supply s[-1] explicitly when the original signal length was odd.

Parameters

inputTensor

Complex Hermitian tensor (frequency domain) of any shape, typically the output of rfftn.

sint or sequence of int= None

Full output signal length(s) along each transformed axis. The last element is the real (time-domain) length of the last transformed axis. For all other axes s[i] may equal the corresponding input axis length. If None, the last axis output length defaults to

2 (m - 1)

where

m

is the input last-axis length; all other axes keep their input sizes.

dimint or sequence of int= None

Axis or axes over which to compute the inverse transform. Defaults to all axes.

normstr or None= None

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

Returns

Tensor

Real tensor (float32) whose shape matches input except:

The last transformed axis has length s[-1] (or $2(m-1)$ by default, where $m$ is the input last-axis length).
All other transformed axes have lengths s[i] (or input sizes when s is None).

Notes

Specifying odd-length signals — if the original real signal had an odd length $N$ (so the rfft output had $(N+1)/2$ bins), you must pass s=[N] explicitly. Without it the default $2(m-1)$ rule would give $N-1$ (even), producing the wrong output length.

Round-trip — for a real tensor x:

\text{irfftn}(\text{rfftn}(x, \text{norm}=m), s, \text{norm}=m) \approx x

where s should contain the original axis sizes to avoid the even/odd ambiguity.

Examples

Round-trip through the real FFT:
>>> x = lucid.randn(128)
>>> X = lucid.fft.rfftn(x)
>>> X.shape
(65,)
>>> x_rec = lucid.fft.irfftn(X, s=[128])
>>> x_rec.shape
(128,)
3-D round-trip:
>>> x = lucid.randn(16, 32, 64)
>>> X = lucid.fft.rfftn(x)
>>> x_rec = lucid.fft.irfftn(X, s=[16, 32, 64])
>>> x_rec.shape
(16, 32, 64)