In
theoretical computer science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation.
It is difficult to circumscribe the theoretical areas precisely. The Associati ...
, a discrete system is a system with a
countable
In mathematics, a Set (mathematics), set is countable if either it is finite set, finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function fro ...
number of
state
State most commonly refers to:
* State (polity), a centralized political organization that regulates law and society within a territory
**Sovereign state, a sovereign polity in international law, commonly referred to as a country
**Nation state, a ...
s. 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
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discret ...
and is analyzed for correctness and
complexity
Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.
The term is generally used to c ...
according to
computational theory
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., app ...
. Because discrete systems have a countable number of states, they may be described in precise
mathematical models.
A
computer
A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
is a
finite-state machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...
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
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "poi ...
intervals.
See also
*
Digital control
Digital control is a branch of control theory that uses Digital data, digital computers to act as system controllers.
Depending on the requirements, a digital control system can take the form of a microcontroller to an Application-specific integr ...
*
Finite-state machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...
*
Frequency spectrum
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed int ...
*
Mathematical model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
*
Sample and hold
In electronics, a sample and hold (also known as sample and follow) circuit is an analog device that samples (captures, takes) the voltage of a continuously varying analog signal and holds (locks, freezes) its value at a constant level for a ...
*
Sample rate
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples".
A sample is a value of the signal at a point in time and/or ...
*
Sample time
*
Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain or z-plane) representation.
It can be considered a dis ...
References
*
*
Automata (computation)
Models of computation
Signal processing
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