The Sampling Theorem

This lecture covers the sampling theorem, starting with the space of bandlimited functions and the concept of sampling as a basis expansion. It then delves into the analysis and synthesis formulas, highlighting the basis functions in the space of bandlimited functions. The lecture concludes with the corollary of the sampling theorem, emphasizing the sufficient representation of signals in the frequency domain. The instructor explains how signals can be sampled without loss of information, introducing the Nyquist frequency as a critical parameter.