# EEG signal processing with sampling frequency

What is the relation between sampling frequency and the frequency of the signal after sampling? For example sampling frequency is 100 Hz, that is the signal contain maximum frequency of 50 Hz. Then what will be the maximum frequency after sampling? Is it 100 or 50? Or it is above it? How can we see it in MATLAB?

Intuitively... Assume to have a sampled signal, i.e. a sequence $\{s(n)\}$. The "fastest" oscillatory behaviour you can see is a component which changes "polarity" at any successive sample, for example consider $$s(n) = (-1)^n$$
it is positive for $n=0$, negative for $n=1$, positive again for $n=2$ and so on. Trivially you cannot have something oscillating faster. The period of this signal is 2 (samples), infact you have $s(n) = s(n+2)$ for any $n$. Therefore its frequency is half the sampling frequency.