A time-variant system is a

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...

whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior. Time variant systems respond differently to the same input at different times. The opposite is true for time invariant systems (TIV).

Overview

There are many well developed techniques for dealing with the response of linear time invariant systems, such as

Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

and

Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

s. However, these techniques are not strictly valid for time-varying systems. A system undergoing slow time variation in comparison to its time constants can usually be considered to be time invariant: they are close to time invariant on a small scale. An example of this is the aging and wear of electronic components, which happens on a scale of years, and thus does not result in any behaviour qualitatively different from that observed in a time invariant system: day-to-day, they are effectively time invariant, though year to year, the parameters may change. Other linear time variant systems may behave more like nonlinear systems, if the system changes quickly – significantly differing between measurements. The following things can be said about a time-variant system: * It has explicit dependence on time. * It does not have an

impulse response In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reac ...

in the normal sense. The system can be characterized by an impulse response except the impulse response must be known at each and every time instant. * It is not stationary in the sense of constancy of the signal's distributional frequency. This means that the parameters which govern the signal's process exhibit varaition with the passage of time. See Stationarity (statistics) for in-depth theoretics regarding this property.

Linear time-variant systems

Linear-time variant (LTV) systems are the ones whose parameters vary with time according to previously specified laws. Mathematically, there is a well defined dependence of the system over time and over the input parameters that change over time. :

y(t) = f ( x(t), t)

In order to solve time-variant systems, the algebraic methods consider initial conditions of the system i.e. whether the system is zero-input or non-zero input system.

Examples of time-variant systems

The following time varying systems cannot be modelled by assuming that they are time invariant: * The Earth's thermodynamic response to incoming Solar irradiance varies with time due to changes in the Earth's

albedo Albedo ( ; ) is the fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...

and the presence of

greenhouse gas Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. Unlike other gases, greenhouse gases absorb the radiations that a planet emits, resulting in the greenhouse effect. T ...

es in the atmosphere. * Discrete wavelet transform, often used in modern signal processing, is time variant because it makes use of the decimation operation{{dubious, date=July 2021.

References

Control theory

Overview

Linear time-variant systems

Examples of time-variant systems

See also

References