I have a question about Sampling Theorem. Sampling Theorem states that a "band-limited" signal can be exactly reproduced if it is sampled at a frequency F, where F is greater than twice the maximum frequency in the signal.
But mathematically, a signal can never be truly band-limited. A law of Fourier transformations says that if a signal is finite in time, its spectrum extends to infinite frequency, and if its bandwidth is finite, its duration is infinite in time. Clearly we cannot have a time-domain signal of infinite duration, so we can never have a truly band-limited signal.
My question is that, how do we calculate the sampling rate for a real signal, that's not not band-limited?