Zeitvariante

Zeitvariante is a German term used to describe phenomena, systems, or models whose defining properties change over time. The adjective form zeitvariant denotes that a characteristic is not constant but evolves, in contrast to zeitstabil oder zeitinvariant, where properties remain unchanged under time shifts. In some contexts the term is exchanged with zeitabhängig or zeitlich variabel.

In signal processing and control theory, zeitvariante systems are called linear time-variant (LTV) systems. Such systems do not have a fixed impulse response. Instead, their response depends on both the observation time and the time of the input. Mathematically, the output y(t) for an input x(t) can be expressed with a time-variant kernel h(t, τ): y(t) = ∫ h(t, τ) x(τ) dτ. This contrasts with linear time-invariant systems, where the impulse response h depends only on the difference t−τ. Zeitvariante models are essential when system parameters evolve, such as changing gains, delays, or filtering characteristics.

Common domains where zeitvariante concepts appear include wireless communications with moving receivers, acoustics in changing environments, and dynamic systems with wear or adaptive control. In probability and statistics, non-stationary processes are time-variant in their statistical properties, such as mean or variance depending on time.

Terminology varies by field; some authors prefer zeitabhängig or zeitlich variabel, but zeitvariante emphasizes the explicit time-dependence of system behavior.