Aliasing and the Sampling Theorem

We have learned that spectral aliases arise after sampling at integer multiples of the sample rate $f_s$. An example of this is shown in the figure below:

We’ll now look at the sampling theorem, which puts a fundamental limit on the sample rate for signal representation in discrete time.

Background

How should we choose the sample rate $f_s$?

• We know that a closer time spacing, i.e., a smaller $T_s$, produces a better approximation of the signal in discrete time and pushes the spectral aliases further away due to the large $f_s$

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