torch.fft.ihfftn

torch.fft.ihfftn(input, s=None, dim=None, norm=None, *, out=None) → Tensor

Computes the N-dimensional inverse discrete Fourier transform of real input.

input must be a real-valued signal, interpreted in the Fourier domain. The n-dimensional IFFT of a real signal is Hermitian-symmetric, X[i, j, ...] = conj(X[-i, -j, ...]). ihfftn() represents this in the one-sided form where only the positive frequencies below the Nyquist frequency are included in the last signal dimension. To compute the full output, use ifftn().

Note

Supports torch.half on CUDA with GPU Architecture SM53 or greater. However it only supports powers of 2 signal length in every transformed dimensions.

Parameters:

• input (Tensor) – the input tensor

• s (Tuple[int], optional) – Signal size in the transformed dimensions. If given, each dimension dim[i] will either be zero-padded or trimmed to the length s[i] before computing the Hermitian IFFT. If a length -1 is specified, no padding is done in that dimension. Default: s = [input.size(d) for d in dim]

• dim (Tuple[int], optional) – Dimensions to be transformed. Default: all dimensions, or the last len(s) dimensions if s is given.

• norm (str, optional) –

  Normalization mode. For the backward transform (ihfftn()), these correspond to:

  • "forward" - no normalization

  • "backward" - normalize by 1/n

  • "ortho" - normalize by 1/sqrt(n) (making the Hermitian IFFT orthonormal)

  Where n = prod(s) is the logical IFFT size. Calling the forward transform (hfftn()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make ihfftn() the exact inverse.

  Default is "backward" (normalize by 1/n).

Keyword Arguments:

out (Tensor, optional) – the output tensor.

Example

>>> T = torch.rand(10, 10)
>>> ihfftn = torch.fft.ihfftn(T)
>>> ihfftn.size()
torch.Size([10, 6])

Compared against the full output from ifftn(), we have all elements up to the Nyquist frequency.

>>> ifftn = torch.fft.ifftn(t)
>>> torch.allclose(ifftn[..., :6], ihfftn)
True

The discrete Fourier transform is separable, so ihfftn() here is equivalent to a combination of ihfft() and ifft():

>>> two_iffts = torch.fft.ifft(torch.fft.ihfft(t, dim=1), dim=0)
>>> torch.allclose(ihfftn, two_iffts)
True