THE SAMPLING THEOREM
Theorem: If the highest frequency contained in an analog signal x_a(t) is F_max = B, and the signal is sampled at a frequency F_s > 2B, then the analog signal can be exactly recovered from its samples using the following reconstruction formula:
Note that at the original sample instances (t = nT), the reconstructed analog signal is equal to the value of the original analog signal because the sinc functions take on values of zero at multiples of the sample period. At times between the sample instances, the signal is the weighted sum of shifted sinc functions.