# Analog and Digital Conversion/Sampling Theorem

From Wikibooks, open books for an open world

## Sampling Theorem[edit]

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[edit]

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:

Where is the sampled value at time T.