Inverse Hartley transform for creating a GP covariance kernel based on a Fourier power spectrum
The demo of https://gitlab.mpcdf.mpg.de/ift/nifty/-/blob/NIFTy_8/demos/re/hmc_wiener_filter.py
uses jft.correlated_field.hartley
to create a covariance kernel from a powerlaw Fourier power spectrum.
My understanding is that an inverse Hartley transform would be needed to make the connection, since the Fourier power spectrum is obtained by a Fourier transform.
However, in https://gitlab.mpcdf.mpg.de/ift/nifty/-/blob/NIFTy_8/src/re/correlated_field.py#L23 the "hartley" function is implemented with a (forward) FFT and summing real and imaginary components.
Why is that equivalent to an inverse Hartley transform?