torch.fft.ihfft2

torch.fft.ihfft2(input, s=None, dim=(- 2, - 1), norm=None, *, out=None) → Tensor

Computes the 2-dimensional inverse discrete Fourier transform of real input. Equivalent to ihfftn() but transforms only the two last dimensions by default.

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: last two dimensions.

• norm (str, optional) –

  Normalization mode. For the backward transform (ihfft2()), 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 (hfft2()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make ihfft2() the exact inverse.

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

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example

>>> T = torch.rand(10, 10)
>>> t = torch.fft.ihfft2(t)
>>> t.size()
torch.Size([10, 6])

Compared against the full output from ifft2(), the Hermitian time-space signal takes up only half the space.

>>> fftn = torch.fft.ifft2(t)
>>> torch.allclose(fftn[..., :6], rfftn)
True

The discrete Fourier transform is separable, so ihfft2() here is equivalent to a combination of ifft() and ihfft():

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