My recollection from text "Random Data: Analysis and Measurement Procedures" by Bendat & Piersol, the theoretical minimum sampling rate is 2.4 times the highest frequency of interest. However from practical experience, i found that to obtain reliable & consistent results, applying a 5x the highest frequency of interest gave much more reproducible results; so if your definition of beta is up to 30 Hz then 200 Hz sampling should be sufficient.

The Nyquist-Shannon theorem (https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem) states that "if a signal containing no frequency higher than fN is sampled at a frequency at least twice the fN , the signal can be reconstructed without loss from its samples". The frequency fN is called the Nyquist frequency. Practical rule following from the theorem can be formulated as "a signal sampled at a sampling rate fs can be fully reconstructed from its samples without loss if the signal contains only frequencies lower than fN = fs/2".

Important, but often misrepresented part of the theorem is the condition of "signal containing no frequency higher than fN". Sometimes you can find statements like "if a signal is sampled at a sampling rate fs, such that fs is at least twice the highest frequency of interest, this frequency of interest can be fully recovered from the samples". This statemt is wrong, because if the signal does contain frequencies above fs/2, even the frequencies below fs/2 cannot be precisely recovered due to the aliasing (https://en.wikipedia.org/wiki/Aliasing).

So, to answer your question, the sampling rate of 200 Hz is sufficient to analyse any EEG frequencies below Niquist frequency of 100 Hz (= 200/2) if, before sampling, the EEGs were low-pass filtered to guarantee that the signals did not contain any frequencies higher than 100 Hz. Practically speaking, check that the EEGs were appropriately filtered before digitization, and if they were, your sampled data is certainly good to analyze the 30Hz beta range.

Franklin Lue Thanks for the explanation and sharing of your experience!

Vladimir Y Vildavski Thanks for the clear explanations with the links. May I also ask what you refer to by "check that the EEGs were appropriately filtered before digitization"?

Thus far, the first few steps of my pre-processing pipeline is as follows:

1. import raw EEG file

2. add channel location

3. apply bandpass filter (1 - 30 Hz) on the raw EEG data

4. reject noisy channels

5. average re-reference

(etc)

Thanks in advance!

"... check that the EEGs were appropriately filtered before digitization":

To prevent aliasing, any frequencies higher than Nyquist frequency (100 Hz in your case) should be removed from the signal prior to digitization. This is done by analog low-pass filtering or some equivalent techniques.

How to check? This depends on the equipment used for recording your dataset. If it was a commercial EEG system that saved the signals in digital form – do not worry, these systems usually automatically take care of necessary filtering. However, if the EEGs were recorded using analog amplifiers and a separate ADC converter, the low-pass filter on the amplifiers had to be set at a cut-off frequency below 100 Hz prior to digitization.

Vladimir Y Vildavski okie got it! Thanks a lot :)