Nyquist–Shannon sampling theorem in the context of "Band-limiting"

In digital recording, an audio or video signal is converted into a stream of discrete numbers representing the changes over time in air pressure for audio, or chroma and luminance values for video. This number stream is saved to a storage device. To play back a digital recording, the numbers are retrieved and converted back into their original analog audio or video forms so that they can be heard or seen.

In a properly matched analog-to-digital converter (ADC) and digital-to-analog converter (DAC) pair, the analog signal is accurately reconstructed, within the constraints of the Nyquist–Shannon sampling theorem, which dictates the sampling rate and quantization error dependent on the audio or video bit depth. Because the signal is stored digitally, assuming proper error detection and correction, the recording is not degraded by copying, storage or interference.

In signal processing, the Nyquist rate, named after Harry Nyquist, is a value equal to twice the highest frequency (bandwidth) of a given function or signal. It has units of samples per unit time, conventionally expressed as samples per second, or hertz (Hz). When the signal is sampled at a higher sample rate (see § Critical frequency), the resulting discrete-time sequence is said to be free of the distortion known as aliasing. Conversely, for a given sample rate the corresponding Nyquist frequency is one-half the sample rate. Note that the Nyquist rate is a property of a continuous-time signal, whereas Nyquist frequency is a property of a discrete-time system.

The term Nyquist rate is also used in a different context with units of symbols per second, which is actually the field in which Harry Nyquist was working. In that context it is an upper bound for the symbol rate across a bandwidth-limited baseband channel such as a telegraph line or passband channel such as a limited radio frequency band or a frequency division multiplex channel.