Discrete-time signal

A discrete-time signal, sometimes referred to simply as a discrete signal, is a special form of a signal, which is defined only at certain, usually periodic times. It is recovered from a continuous time signal by a time-continuous signal profile at certain times, a signal value is taken. Each signal value is worth continuously and can be arbitrarily accurate in its resolution. A discrete-time signal can then by an additional quantization of the individual signal values ​​, which means a reduction of the numerical range for a certain, finite number of levels, is converted into a digital signal.

Discrete-time signals play an important role in signal theory and information technology for system description and as a precursor to digital signal processing.

General

A discrete-time signal can be described mathematically by real numbers as a sequence x [ n]. The index n is the time variable normalized to the sampling rate - usually takes place at constant sampling intervals Ts, the reciprocal is referred to as sampling rate or sampling frequency fs. The values ​​of the time-discrete signal between two sampling instants, and are not zero, but are not defined.

The Nyquist-Shannon sampling theorem, in this case describes the effect that, in the sequence x [n] then the complete information of the continuous signal waveform is included, when the highest -frequency components are smaller than half the sampling frequency fa fs:

A continuous signal can be represented as an example and in the right figure, by the function

Are described. The derived discrete-time signal is featuring with red vertical lines and can be expressed as: