torch.fft.rfft2

torch.fft.rfft2(input, s=None, dim=(- 2, - 1), norm=None, *, out=None) → Tensor

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

The FFT of a real signal is Hermitian-symmetric, X[i, j] = conj(X[-i, -j]), so the full fft2() output contains redundant information. rfft2() instead omits the negative frequencies in the last dimension.

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 real FFT. 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 forward transform (rfft2()), these correspond to:

  • "forward" - normalize by 1/n

  • "backward" - no normalization

  • "ortho" - normalize by 1/sqrt(n) (making the real FFT orthonormal)

  Where n = prod(s) is the logical FFT size. Calling the backward transform (irfft2()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make irfft2() the exact inverse.

  Default is "backward" (no normalization).

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example

>>> t = torch.rand(10, 10)
>>> rfft2 = torch.fft.rfft2(t)
>>> rfft2.size()
torch.Size([10, 6])

Compared against the full output from fft2(), we have all elements up to the Nyquist frequency.

>>> fft2 = torch.fft.fft2(t)
>>> torch.testing.assert_close(fft2[..., :6], rfft2, check_stride=False)

The discrete Fourier transform is separable, so rfft2() here is equivalent to a combination of fft() and rfft():

>>> two_ffts = torch.fft.fft(torch.fft.rfft(t, dim=1), dim=0)
>>> torch.testing.assert_close(rfft2, two_ffts, check_stride=False)