# Discrete system

__: System with a countable number of states__

**Short description**In theoretical computer science, a **discrete system** is a system with a countable number of states. Discrete systems may be contrasted with continuous systems, which may also be called analog systems. A final discrete system is often modeled with a directed graph and is analyzed for correctness and complexity according to computational theory. Because discrete systems have a countable number of states, they may be described in precise mathematical models.

A computer is a finite state machine that may be viewed as a discrete system. Because computers are often used to model not only other discrete systems but continuous systems as well, methods have been developed to represent real-world continuous systems as discrete systems. One such method involves sampling a continuous signal at discrete time intervals.

## See also

- Digital control
- Finite state machine
- Frequency spectrum
- Mathematical model
- Sample and hold
- Sample rate
- Sample time
- Z-transform

## References

- Hopcroft, John E.; Rajeev Motwani; Jeffrey D. Ullman (2001).
*Introduction to Automata Theory, Languages, and Computation*(2nd ed.). Reading Mass: Addison-Wesley. ISBN 0-201-44124-1. - Benjamin C. Kuo (1995).
*Digital Control Systems*(2nd ed.). USA: Oxford University Press. ISBN 0-19-512064-7.

Original source: https://en.wikipedia.org/wiki/Discrete system.
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