torch.fft.ihfftn¶
- torch.fft.ihfftn(input, s=None, dim=None, norm=None, *, out=None) Tensor ¶
Computes the N-dimensional inverse discrete Fourier transform of real
input
.input
must be a real-valued signal, interpreted in the Fourier domain. The n-dimensional IFFT of a real signal is Hermitian-symmetric,X[i, j, ...] = conj(X[-i, -j, ...])
.ihfftn()
represents this in the one-sided form where only the positive frequencies below the Nyquist frequency are included in the last signal dimension. To compute the full output, useifftn()
.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 dimension
dim[i]
will either be zero-padded or trimmed to the lengths[i]
before computing the Hermitian IFFT. 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: all dimensions, or the last
len(s)
dimensions ifs
is given.norm (str, optional) –
Normalization mode. For the backward transform (
ihfftn()
), these correspond to:"forward"
- no normalization"backward"
- normalize by1/n
"ortho"
- normalize by1/sqrt(n)
(making the Hermitian IFFT orthonormal)
Where
n = prod(s)
is the logical IFFT size. Calling the forward transform (hfftn()
) with the same normalization mode will apply an overall normalization of1/n
between the two transforms. This is required to makeihfftn()
the exact inverse.Default is
"backward"
(normalize by1/n
).
- Keyword Arguments:
out (Tensor, optional) – the output tensor.
Example
>>> T = torch.rand(10, 10) >>> ihfftn = torch.fft.ihfftn(T) >>> ihfftn.size() torch.Size([10, 6])
Compared against the full output from
ifftn()
, we have all elements up to the Nyquist frequency.>>> ifftn = torch.fft.ifftn(t) >>> torch.allclose(ifftn[..., :6], ihfftn) True
The discrete Fourier transform is separable, so
ihfftn()
here is equivalent to a combination ofihfft()
andifft()
:>>> two_iffts = torch.fft.ifft(torch.fft.ihfft(t, dim=1), dim=0) >>> torch.allclose(ihfftn, two_iffts) True