When it comes to preprocessing of EEG data, the first step is to filter the signal. Filtering is done such that it preserves information across different bands of the EEG data (alpha, beta, gamma, delta). Typically, many researchers use 0.5 - 50 Hz band in the first step (removes DC components). Note that the filter should be zero-phase such that no delay or phase changes are introduced in the EEG data on using the filter. One simple way is to use
filtfilt command in MATLAB.
In addition, a notch filter is also designed to remove 60 Hz. You might be wondering why we need a notch filter at 60 Hz if we are filtering the original signal using a band-pass filter of 0.5 - 50 Hz. To answer this, we need to first understand the structure of the band-pass filter. If the band-pass filter is of lower order, then the transition bands are not very steep (or sharp). This in turn introduces some part of the 60 Hz interference into the band-pass filtered signal (which typically dominates in EEG data). So, to suppress the strong 60 Hz interference, a notch filter is also used.
After filtering the EEG data using a band-pass and a notch filter, you might want to address different types of artifacts that show up in the EEG data. Some of the them include EKG artifact, movement artifact, sweat artifact, etc. Each artifact removal requires a sophisticated approach such that the EEG data is preserved but the artifact is removed completely.