Time domain

{{Short description|Analysis of math functions with respect to time}} In [[mathematics]] and [[signal processing]], the '''time domain''' is a representation of how a signal, function, or data set varies with time.{{Cite web |date=2024-07-17 |title=Time Domain Analysis vs Frequency Domain Analysis: A Guide and Comparison |url=https://resources.pcb.cadence.com/blog/2020-time-domain-analysis-vs-frequency-domain-analysis-a-guide-and-comparison |access-date=2025-02-16 |website=resources.pcb.cadence.com |language=en-US}} It is used for the analysis of [[function (mathematics)|mathematical functions]], physical [[signal (information theory)|signal]]s or [[time series]] of [[economics|economic]] or [[environmental statistics|environmental]] data.

In the time domain, the [[independent variable]] is time, and the [[dependent variable]] 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]]s representing time. For [[Discrete time and continuous time|discrete-time]] signals, the value is known at discrete, often equally-spaced, time intervals.{{Cite web |title=Discrete Time Signal: Know Definition, Classification, Representation & Applications |url=https://testbook.com/electrical-engineering/discrete-time-signal |access-date=2025-02-16 |website=Testbook |language=en}} It is commonly visualized using a graph where the x-axis represents time and the y-axis represents the signal's value.{{Cite web |title=Definition of time domain |url=https://www.photonics.com/EDU/time_domain/d8234 |access-date=2025-02-16 |website=Photonics.com}} 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 (geometry)|position]] in [[space]] when dealing with [[Spatial frequency|spatial frequencies]], as a substitute for the more precise term ''spatial domain''.[[File:Fourier_transform_time_and_frequency_domains_(small).gif|frame|right|The [[Fourier transform]] relates the function in the time domain, shown in red, to the function in the frequency domain, shown in blue. The component frequencies, spread across the frequency spectrum, are represented as peaks in the frequency 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.{{cite journal |first1=Y. W. |last1=Lee | first2=T. P. Jr. |last2=Cheatham |first3=J. B. |last3=Wiesner |year=1950 |title=Application of Correlation Analysis to the Detection of Periodic Signals in Noise |journal=Proceedings of the IRE |volume=38 |issue=10 |pages=1165–1171 |doi=10.1109/JRPROC.1950.233423 |s2cid=51671133 }} When an analysis uses the [[second]] or one of its multiples as a [[unit of measurement]], then it is in the time domain. When analysis concerns the reciprocal units such as [[Hertz]], then it is in the frequency domain.

== See also ==

• [[Frequency domain]]
• [[Fourier transform]]
• [[Laplace transform]]
• [[Blackman–Tukey transformation|Blackman–Tukey transform]]

== References == {{reflist}}

{{Statistics|analysis}}

[[Category:Time domain analysis]]