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I am a beginner in signal processing. I have two resting eye closed data groups with group 1 having 40 data samples and group 2 having 100 samples. Both are taken from different devices with different frequency sampling rates (1024 vs 500), different number of channels(64 vs 32), different montage system (10-10 vs 10-20), etc but are eye closed.

I am comparing the frequency of average of all data samples across all channels in group 1 vs frequency of average of all data samples across all channels in group 2.

For that I have:

Step 1. For group 1 data(all 40 data samples): Did bandpass filtering for suggested frequency band, average re-referenced them around 32 channels.

For group 2 data(all 100 data samples): We dropped extra channels (converted from 64 to 32) keeping montage the same, cropped the data from beginning and end to make the time duration equal to group 1 data samples, resampled them from 1024 to 500Hz, did similar band pass filtering as in group 1, did not do re referencing as they were already average re-referenced around their 64 channels.

Questions: Instead of dropping 32 channels can we do some operation that converts 64 channels 10-10 montage to 32 channels 10-20 montage? Do we need to do re referencing again for group 2 data samples? If we will be doing wavelet denoising for each data in both groups, will we manually set wavelet, level and threshold for each sample or it will be same for all?

Step 2. Averaged all 40 preprocessed data for group 1 and converted it in a single data and similarly, averaged all 100 preprocessed data for group 2 and converted it in a single data.

Questions: Is averaging a good method, if not what other methods can we apply? What will be effects of averaging data samples before preprocessing vs after preprocessing?

Step 3: Comparing average of PSDs for both group's data (averaging all 32 channels) using welch.

Questions: Is average of power a good method to find differences in both group's frequency bands?

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I would be wary about treating your data differently. If you have 64 recording sites, you can possibly use all 64 channels to get to 32 "less noisy" channels and use that data optimally, but this will also give those recordings different characteristics than data based on fewer original samples (for example, if you do some sort of weighted time-averaging, you're likely to enhance lower frequencies and suppress higher frequencies because lower frequency activity tends to have greater spatial consistency and vice-versa).

I am comparing the frequency of average of all data samples across all channels in group 1 vs frequency of average of all data samples across all channels in group 2.

Don't do this. Presumably, you're interested in some other characteristic besides the recording device and setup. But, your groups are completely confounded with these characteristics. You need a comparable control group. Unless all you want to do is compare the actual recording systems in which case nevermind what I've said. I warn you of this because I'm familiar with these sorts of data and it's common to get very different measurements in the same participants when using different systems (even the same physical depth electrodes connected to different recording systems!). It's okay to have data from different systems when you have both groups recorded on both systems, though you may want to adjust for recording system in the analysis.

For Step 2, I would not average directly; I would use statistical modeling (e.g. regression) to capture the variability in your data while estimating population characteristics. An alternative would be a permutation strategy. But, I would not suggest these in light of your data being recorded in different conditions because of the confounding issue described above.

For Step 3, what does "good method" mean? Appropriate methods depend on the research question and data. Average power is one method; it's going to be less appropriate if there is spatial structure to the data.

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