Editing Linear time-invariant system (section)

=== Discrete-time systems from continuous-time systems ===
In many contexts, a discrete time (DT) system is really part of a larger continuous time (CT) system.  For example, a digital recording system takes an analog sound, digitizes it, possibly processes the digital signals, and plays back an analog sound for people to listen to.

In practical systems, DT signals obtained are usually uniformly sampled versions of CT signals.  If <math>x(t)</math> is a CT signal, then the [[Sample and hold|sampling circuit]] used before an [[analog-to-digital converter]] will transform it to a DT signal:
<math display="block">x_n \mathrel{\stackrel{\text{def}}{=}} x(nT) \qquad \forall \, n \in \mathbb{Z},</math>
where ''T'' is the [[sampling frequency|sampling period]]. Before sampling, the input signal is normally run through a so-called [[anti-aliasing filter|Nyquist filter]] which removes frequencies above the "folding frequency" 1/(2T); this guarantees that no information in the filtered signal will be lost. Without filtering, any frequency component ''above'' the folding frequency (or [[Nyquist frequency]]) is [[Aliasing|aliased]] to a different frequency (thus distorting the original signal), since a DT signal can only support frequency components lower than the folding frequency.