Time-variant system

A time-variant system is a system that is not time invariant (TIV). Roughly speaking, its output characteristics depend explicitly upon time. In other words, a system in which certain quantities governing the system's behavior change with time, so that the system will respond differently to the same input at different times.

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Examples of time-variant systems

The following time varying systems cannot be modelled by assuming that they are time invariant:

• Aircraft – Time variant characteristics are caused by different configuration of control surfaces during take off, cruise and landing as well as constantly decreasing weight due to consumption of fuel.
• The Earth's thermodynamic response to incoming Solar irradiance varies with time due to changes in the Earth's albedo and the presence of greenhouse gases in the atmosphere.
• The human vocal tract is a time variant system, with its transfer function at any given time dependent on the shape of the vocal organs. As with any fluid-filled tube, resonances (called formants) change as the vocal organs such as the tongue and velum move. Mathematical models of the vocal tract are therefore time-variant, with transfer functions often linearly interpolated between states over time.
• Linear time varying processes such as amplitude modulation occur on a time scale similar to or faster than that of the input signal. In practice amplitude modulation is often implemented using time-invariant system nonlinear elements such as diodes.
• The Discrete Wavelet Transform, often used in modern signal processing, is time variant because it makes use of the decimation operation.

See also

• Control system
• Control theory
• System analysis
• Time-invariant system: examples how to prove if a system is time-variant or time-invariant.