hfft(input, n=None, dim=-1, norm=None, *, out=None) → Tensor¶
Computes the one dimensional discrete Fourier transform of a Hermitian symmetric
ihfft()are analogous to
irfft(). The real FFT expects a real signal in the time-domain and gives a Hermitian symmetry in the frequency-domain. The Hermitian FFT is the opposite; Hermitian symmetric in the time-domain and real-valued in the frequency-domain. For this reason, special care needs to be taken with the length argument
n, in the same way as with
Because the signal is Hermitian in the time-domain, the result will be real in the frequency domain. Note that some input frequencies must be real-valued to satisfy the Hermitian property. In these cases the imaginary component will be ignored. For example, any imaginary component in
inputwould result in one or more complex frequency terms which cannot be represented in a real output and so will always be ignored.
The correct interpretation of the Hermitian input depends on the length of the original data, as given by
n. This is because each input shape could correspond to either an odd or even length signal. By default, the signal is assumed to be even length and odd signals will not round-trip properly. So, it is recommended to always pass the signal length
input (Tensor) – the input tensor representing a half-Hermitian signal
n (int, optional) – Output signal length. This determines the length of the real output. If given, the input will either be zero-padded or trimmed to this length before computing the Hermitian FFT. Defaults to even output:
n=2*(input.size(dim) - 1).
dim (int, optional) – The dimension along which to take the one dimensional Hermitian FFT.
norm (str, optional) –
Normalization mode. For the forward transform (
hfft()), these correspond to:
"forward"- normalize by
"backward"- no normalization
"ortho"- normalize by
1/sqrt(n)(making the Hermitian FFT orthonormal)
- Keyword Arguments
out (Tensor, optional) – the output tensor.
Taking a real-valued frequency signal and bringing it into the time domain gives Hermitian symmetric output:
>>> t = torch.arange(5) >>> t tensor([0, 1, 2, 3, 4]) >>> T = torch.fft.ifft(t) >>> T tensor([ 2.0000+-0.0000j, -0.5000-0.6882j, -0.5000-0.1625j, -0.5000+0.1625j, -0.5000+0.6882j])
T == T[-1].conj()and
T == T[-2].conj()is redundant. We can thus compute the forward transform without considering negative frequencies:
>>> torch.fft.hfft(T[:3], n=5) tensor([0., 1., 2., 3., 4.])
irfft(), the output length must be given in order to recover an even length output:
>>> torch.fft.hfft(T[:3]) tensor([0.5000, 1.1236, 2.5000, 3.8764])