I have two EEG signals that are simultaneously recorded during the night (sleep). Imagine one device recorded from channel F4 and the other from Fp2. Now I would like to check the similarity of these signals, so, the first step is to sync them which has been done successfully using cross-correlation :)
I can also report some similarity metrics in time-domain, e.g. Pearson correlation per window (e.g. each 30 s) to quantify the similarity of signals.
The problem arises when I want to compare (or let's say quantify) them in the freq domain. When I plot e.g. spectrogram or PSD we can see their similarity visually; however, I don't know how to quantify this similarity in the frequency domain. By vision the spectrograms (or PSDs) are quite similar but I guess it is not a powerful reason without reporting any similarity metric as a number. Is there any metric by which I can report similarity of PSDs or spectrograms window-by-window and based on each frequency bin (Delta, Theta, etc)?