timedomain

Timedomain, usually written as time domain, refers to the representation and analysis of signals with respect to time. In continuous-time form, a signal is a function x(t) of a real variable t that indicates amplitude at each instant. In discrete time, signals are defined at a sequence of sampling instants x[n]. The time-domain view emphasizes how signals evolve over time and how systems respond to inputs, including delays, transients, and damping.

For linear time-invariant systems, the relationship between input x(t) and output y(t) is described by convolution y(t) = x(t) * h(t), where h(t) is the impulse response. In discrete time, the convolution sums replace integrals. Time-domain analysis often uses differential equations for continuous systems and difference equations for discrete systems.

Time-domain data can be analyzed directly or transformed into other domains. The Fourier transform relates time-domain signals to their frequency content; the Laplace transform and z-transform extend analysis to complex frequency domains and aid system characterization. Many problems are approached by switching between time and frequency domains or by hybrid time–frequency methods.

Applications include electronics and signal processing (observing waveforms with oscilloscopes), communications, control systems, audio engineering, seismology, and time-domain reflectometry for locating faults in cables. The time-domain perspective is essential for understanding transients, stability, and real-time behavior of dynamic systems.