In
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. ...
of
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 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, where the signal is represented by its constituent frequencies. For
continuous-time 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 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 is a common tool used to visualize real-world signals in the time domain.
Though most precisely referring to
time in physics, 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 ''
frequency domain'' developed in U.S.
communication engineering in the late 1940s, with the terms appearing together without definition by 1950.
When an analysis uses the
second 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.
See also
*
Frequency domain
*
Fourier transform
*
Laplace transform
*
Blackman–Tukey transform
References
{{Statistics, analysis
Time domain analysis