mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...

, the time domain is a representation of how a signal, function, or data set varies with time. It is used for the analysis of mathematical functions, physical

signal A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

s or

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. ...

economic An economy is an area of the Production (economics), production, Distribution (economics), distribution and trade, as well as Consumption (economics), consumption of Goods (economics), goods and Service (economics), services. In general, it is ...

or environmental data. In the time domain, the

independent variable A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function ...

is time, and the

dependent variable A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical functio ...

is the value of the signal. This contrasts with the

frequency domain In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time ser ...

, where the signal is represented by its constituent frequencies. For

continuous-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 ...

signals, the value of the signal is defined for all

real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...

s representing time. For

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 ...

signals, the value is known at discrete, often equally-spaced, time intervals. It is commonly visualized using a graph where the x-axis represents time and the y-axis represents the signal's value. An

oscilloscope An oscilloscope (formerly known as an oscillograph, informally scope or O-scope) is a type of electronic test instrument that graphically displays varying voltages of one or more signals as a function of time. Their main purpose is capturing i ...

is a common tool used to visualize real-world signals in the time domain. Though most precisely referring to

time in physics In physics, time is defined by its operational definition, measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar (physics), scalar quantity (often denoted by the symbol t) and, like length, mass, and ...

, the term ''time domain'' may occasionally informally refer to position in

space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...

when dealing with spatial frequencies, as a substitute for the more precise term ''spatial domain''.

Origin of term

The use of the contrasting terms ''time domain'' and ''

'' developed in U.S.

communication engineering Telecommunications engineering is a subfield of electronics engineering which seeks to design and devise systems of communication at a distance. The work ranges from basic circuit design to strategic mass developments. A telecommunication engi ...

in the late 1940s, with the terms appearing together without definition by 1950. When an analysis uses the

second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...

or one of its multiples as a

unit of measurement A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other qua ...

, then it is in the time domain. When analysis concerns the reciprocal units such as

Hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...

, then it is in the frequency domain.

References

{{Statistics, analysis Time domain analysis

Origin of term

See also

References