Some Question about Frequency Domain

[khan-yin]

Great Work on the Time series enhanced by frequency information🤩! I noticed that you did not use ifft to change back in time domain, which makes me curious about the reason, it is the first time I saw people directly use the amplitude and phrase.
As the paper mentioned:

"RAINCOAT extracts the polar coordinates of frequency coefficients to keep both low-level (ai) and high-level (pi) semantics. The frequency space features eF is a concatenation [ai; pi]."

Well, I am a student now beginning to focus on Time series OOD. I want to know the low-level (ai) and high-level (pi) semantics information you mentioned means what kind of information in time series. Thesedays, I did some experiments on data augmentations for OOD Domain generalization, and I noticed that low-frequency is more important than high-frequency. I want to explore whether there are some common invariants behind the frequency domain, so the amplitude and phrase are naturally to be considered.
I think there are must some connections between low/high frequency and [amplitude and phrase], but my knowledge of maths and experimental experience is limited, I might as well take the opportunity to ask you this question🤣