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 radiation varies with time due to changes in the Earth's albedo and the presence of greenhouse gasses 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 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.
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