# Discrete time and continuous time

discrete-timediscrete timecontinuous-timecontinuous timediscretecontinuous signaldiscrete-time signaldiscrete signalcontinuouscontinuous-time signal
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.wikipedia
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### Time series

time series analysistime-seriestime-series analysis
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
Thus it is a sequence of discrete-time data.

### Sampling (signal processing)

sampling ratesamplingsample rate
Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal. By acquiring values of an analog signal at constant or variable rate. This process is called sampling. Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.

### Analog signal

analoganalogueanalogue signal
By acquiring values of an analog signal at constant or variable rate. This process is called sampling.
An analog signal is any continuous signal for which the time-varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal.

### Continuous or discrete variable

continuous variablecontinuousdiscrete variable
Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable.
In continuous-time dynamics, the variable time is treated as continuous, and the equation describing the evolution of some variable over time is a differential equation.

### Quantization (signal processing)

quantizationquantization errorquantized
Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.
Sampling converts a time-varying voltage signal into a discrete-time signal, a sequence of real numbers.

### Signal

signalselectrical signalelectrical signals
A continuous signal or a continuous-time signal is a varying quantity (a signal)
Discrete-time signals are often referred to as time series in other fields.

### Digital signal processing

DSPsignal processingdigital signal processing (DSP)
Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.
Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling.

### Sequence

sequencessequentialinfinite sequence
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
Discrete-time signal

### Discrete system

discretediscrete and continuous systemsdiscrete state
Discrete system
One such method involves sampling a continuous signal at discrete time intervals.

### Excess demand function

where \delta is the positive speed-of-adjustment parameter which is less than or equal to 1, and where f is the excess demand function.
If continuous time is assumed, the adjustment process is expressed as a differential equation such as

### Time-scale calculus

time scale calculusdynamic equations on time scalestime scale
Time-scale calculus
The two most commonly encountered examples of time scales are the real numbers \mathbb{R} and the discrete time scale h\mathbb{Z}.

### Discretization

discretizeddiscretizingdichotomization
Discretization
Discrete time and continuous time

### Mathematics

mathematicalmathmathematician
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

### Dynamical system

dynamical systemsdynamic systemdynamic systems
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

### Variable (mathematics)

variablesvariableunknown
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

### Integer

integersintegralwhole number
Measurements are typically made at sequential integer values of the variable "time".

### Infinitesimal

infinitesimalsinfinitely closeinfinitesimally
In contrast, continuous time views variables as having a particular value for potentially only an infinitesimally short amount of time.

### Infinity

infiniteinfinitely
Between any two points in time there are an infinite number of other points in time.

### Real line

real number linereal axis real numbers
The variable "time" ranges over the entire real number line, or depending on the context, over some subset of it such as the non-negative reals.

### Quantity

quantitiesquantitativeamount
A continuous signal or a continuous-time signal is a varying quantity (a signal)

### Continuum (set theory)

continuumcontinuacontinuous
whose domain, which is often time, is a continuum (e.g., a connected interval of the reals).

### Connected space

connectedconnected componentpath-connected
whose domain, which is often time, is a continuum (e.g., a connected interval of the reals).

### Real number

realrealsreal-valued
whose domain, which is often time, is a continuum (e.g., a connected interval of the reals).

### Uncountable set

uncountableuncountably infiniteuncountably
That is, the function's domain is an uncountable set.

### Continuous function

continuouscontinuitycontinuous map
The function itself need not be continuous.