# 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.