is there any relationships between the 'number of electrodes' and 'quality of analysis' in EEG signal processing ?
You are true in Yours doubts. My own opinion is that EEG-signal is near pink noise. Single pair of electrodes produces Compex random signal depending on filters adjustments. N-pair electrodes produces N-power Complex random signal.
Basic logic is to keep signal simple to extract fruitful information. No doubt adding more electrode more signals you will acquire, but as per my experience anything above 6 does not add significant piece of information (Just like adding a drop more in already full glass)
Your question is related to the sampling theorem. In time domain analysis you would ask "how fast do I need to sample a signal not to lose information"? The answer is the expression of the famous Nyquist criterion, and depends on how fast your signal changes along time: For a signal which is band-limited in frequency to fmax (that is, its power spectrum P(f) is zero for f > fmax), you need to sample at a frequency above 2*fmax.. You are just asking the same question, but instead of time, you have space, that is, "how close my electrodes have to be" to sample the EEG and not lose information? The answer is of course dependant on how fast your signal varies along space. The answer can be found by (I) oversample the EEG along space; (ii) perform a spectrum analysis of the EEG (FFT) to find at what special frequency (measured in per cm, rather than per second) it drops to zero (or a very small 'noise floor' level). There you have the value that will be your Nyquist spatial frequency, say 1/(2 cm), and you need to sample at a frequency more than twice that (or have the electrodes closer than half of that distance), that is your electrodes would have to be closer than one every 1 cm (half the spatial period, or twice the spatial frequency). It is very simple and any good book on EEG should tell you that.
See http://dx.doi.org/10.1016/S1388-2457(03)00045-2
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