Comparing similarity of two simultaneously recorded EEGs in freq domain

Thanks again @A_A! Yes, I am using exactly the same function (scipy.signal.coherence). I have a roughly flat coherence over all frequencies (f > 5Hz) which is good: it means that the 2nd device doesn't magnify some specific freqs unnecessarily and have the same similarity with device 1 over all freq ranges.

Just as a short recap: my aim is to kind of prove that 2nd EEG device collects similar signals with respect to the ground truth (EEG device 1) --> So device 2 can be used also as a reliable EEG recorder. Please note that device 1 has an electrode at Fp1 location, though the electrode of device 2 was placed at F4 location, so we cannot expect extremely high correlation or coherence (I guess, right?).

My problem now is that the mean of coherence plot is around 0.20, however, I had almost 0.5 and 0.40 when talking about Pearson correlation and spearman, respectively. Does this difference between coherence and time-domain correlations (pearson or spearman) make sense? Can we accept 20% coherence as an acceptable value that the both signals are similar? I know that the pearson of 50% shows a good similarity, but I have no clue about coherence (and couldn't find anywhere any clear answer to this).

I show the coherence plot during different sleep stages and different freq bins bellow: Coherence between F4 (EEG device 1) and Fp2 (EEG device 2) during sleep. Freq range of interest is 0-30 Hz. Coherence is calculated over windows of 5 seconds.

You can express correlation in the frequency domain but the closest thing to what you are describing would be Coherence.

It returns a number between 0 and 1 per each frequency bin of the spectrum. The closest this number is to 1 the more "similar" the signals would be and you can average this number over the whole spectrum or over a frequency range.

Hope this helps.