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 realinput.Equivalent torfftn() 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 fullfft2() output contains redundant information.rfft2() instead omits the negative frequencies in the lastdimension.

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 dimensiondim[i] will either be zero-padded ortrimmed to the lengths[i] before computing the real FFT.If a length-1 is specified, no padding is done in that dimension.Default:s=[input.size(d)fordindim]

• 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 by1/n

  • "backward" - no normalization

  • "ortho" - normalize by1/sqrt(n) (making the real FFT orthonormal)

  Wheren=prod(s) is the logical FFT size.Calling the backward transform (irfft2()) with the samenormalization mode will apply an overall normalization of1/n betweenthe two transforms. This is required to makeirfft2()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 fromfft2(), we have allelements 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, sorfft2()here is equivalent to a combination offft() andrfft():

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