torch.fft.fft

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

Computes the one dimensional discrete Fourier transform of input.

Note

The Fourier domain representation of any real signal satisfies the Hermitian property: X[i] = conj(X[-i]). This function always returns both the positive and negative frequency terms even though, for real inputs, the negative frequencies are redundant. rfft() returns the more compact one-sided representation where only the positive frequencies are returned.

Note

Supports torch.half and torch.chalf on CUDA with GPU Architecture SM53 or greater. However it only supports powers of 2 signal length in every transformed dimension.

Parameters

• input (Tensor) – the input tensor

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

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

• norm (str, optional) –

  Normalization mode. For the forward transform (fft()), 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 (ifft()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make ifft() 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.fft(t)
tensor([ 6.+0.j, -2.+2.j, -2.+0.j, -2.-2.j])

>>> t = torch.tensor([0.+1.j, 2.+3.j, 4.+5.j, 6.+7.j])
>>> torch.fft.fft(t)
tensor([12.+16.j, -8.+0.j, -4.-4.j,  0.-8.j])