In this lesson you will learn why aliasing occurs when sampling a signal. Aliasing is when a continuous-time sinusoid appears as a discrete-time sinusoid with multiple frequencies. The sampling theorem establishes conditions that prevent aliasing so that a continuous-time signal can be uniquely reconstructed from its samples. The sampling theorem is very important in signal processing. It tells us how fast we have to sample a signal with a given bandwidth to guarantee a unique correspondence between continuous- and discrete-time signals.
This lesson “simplifies” the sampling theorem because it only uses the non uniqueness of discrete-time sinusoids and the mapping between continuous- and discrete-time frequency. The next two lessons take a more conventional Fourier transform based approach to developing the sampling theorem.