torch.fft.rfftn#

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

Computes the N-dimensional discrete Fourier transform of realinput.

The FFT of a real signal is Hermitian-symmetric,X[i_1,...,i_n]=conj(X[-i_1,...,-i_n]) so the fullfftn() output contains redundant information.rfftn() instead omits the negative frequencies in thelast dimension.

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: all dimensions, or the lastlen(s) dimensions ifs is given.

• norm (str,optional) –

  Normalization mode. For the forward transform(rfftn()), 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 (irfftn()) with the samenormalization mode will apply an overall normalization of1/n betweenthe two transforms. This is required to makeirfftn()the exact inverse.

  Default is"backward" (no normalization).

Keyword Arguments:

out (Tensor,optional) – the output tensor.

Example

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

Compared against the full output fromfftn(), we have allelements up to the Nyquist frequency.

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

The discrete Fourier transform is separable, sorfftn()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(rfftn,two_ffts,check_stride=False)