0.1 Shannon's Sampling Theorem

Shannon's seminal work in communication also gave us the sampling theorem that is heavily used over several applications even today. Shannon considers bandlimited signals, possibly owing to his background in the Bell Labs., influenced by speech signals.

Theorem: (Shannon's Sampling Theorem) If a signal $x$ contains no frequencies higher than $f_N$ , it is completely described by giving its ordinates at a series of points spaced $\frac{1}{2f_N}$ apart.

Checkpoint: Think of a proof or proof sketch for the above theorem.