torch.fft.rfft

torch.fft.rfft(input, n=None, dim=- 1, norm=None, *, out=None) → Tensor

Computes the one dimensional Fourier transform of real-valued input.

The FFT of a real signal is Hermitian-symmetric, X[i] = conj(X[-i]) so the output contains only the positive frequencies below the Nyquist frequency. To compute the full output, use fft()

Parameters

• input (Tensor) – the real input tensor

• n (int, optional) – Signal length. If given, the input will either be zero-padded or trimmed to this length before computing the real FFT.

• dim (int, optional) – The dimension along which to take the one dimensional real FFT.

• norm (str, optional) –

  Normalization mode. For the forward transform (rfft()), these correspond to:

  • "forward" - normalize by 1/n

  • "backward" - no normalization

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

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

  Default is "backward" (no normalization).

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example

>>> t = torch.arange(4)
>>> t
tensor([0, 1, 2, 3])
>>> torch.fft.rfft(t)
tensor([ 6.+0.j, -2.+2.j, -2.+0.j])

Compare against the full output from fft():

>>> torch.fft.fft(t)
tensor([ 6.+0.j, -2.+2.j, -2.+0.j, -2.-2.j])

Notice that the symmetric element T[-1] == T[1].conj() is omitted. At the Nyquist frequency T[-2] == T[2] is it’s own symmetric pair, and therefore must always be real-valued.