A breakdown of Nyquist–Shannon sampling theorem

The Nyquist-Shannon sampling theorem is the mathematical theorem which serves as the theoretical framework for Analog-to-Digital signal conversion. The theorem itself establishes a sample rate sufficient for capturing input data from a continuous signal within a finite bandwidth. In other words, the theorem makes it possible to capture an analog signal by sufficiently subdividing it’s values against a graph where the x axis represents time and the y axis represents frequency.

Specifically, the theorem relies on a mathematical function called a Fourier transform. Fourier transform (FT) is a mathematical process through which dimensions of space and time are translated in to time and frequency. It is with the FT that we are able to generate a waveform of an analog (continuous) signal. The sampling theorem itself introduces the concept of a sample rate that is sufficient for perfectly converting the analog signal into digital form.