The definition for discrete-time systems is almost identical to that for continuous-time systems.

To obtain the frequency response of a discrete-time system expressed in the Z domain, we make the substitution .

For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.

The Tinkerbell map is a discrete-time dynamical system given by:

The Duffing map is a discrete-time dynamical system.

The zeros of the discrete-time system are outside the unit circle.

Delay embedding theorems are simpler to state for discrete-time dynamical systems.

The following section derives the matched filter for a discrete-time system.

Transform-domain analysis of discrete-time systems often makes use of the Z transform.

Almost everything in continuous-time systems has a counterpart in discrete-time systems.