# Analog and Digital Conversion/Sampling Theorem

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## Sampling Theorem

The Sampling Theorem is a mathematical construct that allows us to take a single sample of an input waveform at a time T. This is not the same as the star transform.

## Definition

The sampling theorem states that if we convolute the input function with an impulse, centered at the sampling time T, the output will be the value of the input function at time T. More specifically, our output will be the sample at time T. Here is the definition:

${\displaystyle {\bar {f}}(T)=f(t)*\delta (t-T)}$

Where ${\displaystyle {\bar {f}}(T)}$ is the sampled value at time T.