Editing Time-variant system (section)

== Overview ==
There are many well developed [[LTI system theory|techniques]] for dealing with the response of linear time invariant systems, such as [[Laplace transform|Laplace]] and [[Fourier transform]]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&nbsp;– 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 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.