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().

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