Tidsvaryende

Tidsvaryende, or time-varying, is an adjective used to describe systems, processes, or parameters whose properties change over time. It contrasts with time-invariant (constant over time) or stationary situations, where the defining characteristics remain the same regardless of when they are observed.

In mathematics and engineering, tidsvaryende models have coefficients or structures that depend explicitly on time. For example, a linear time-varying system may be described by equations of the form dx/dt = A(t) x + B(t) u, where A(t) and B(t) change with time. The impulse response of such a system depends on both the current time and the time of input, h(t, τ), rather than merely on the difference t − τ. In probability and statistics, tidsvaryende or non-stationary processes have statistical properties, such as mean or variance, that evolve over time.

Applications of tidsvaryende concepts span many fields. In signal processing, time-varying filters adapt to changing signal characteristics. In control theory, adaptive or time-varying controllers handle systems whose dynamics drift over time. Wireless communications must cope with time-varying channels. Climate science, economics, and biology frequently encounter tidsvaryende phenomena, including seasonal patterns, aging components, and evolving market conditions.

Modeling tidsvaryende systems often requires adaptive methods and time-frequency analysis, such asshort-time Fourier transforms or wavelets, as well as Kalman filters or other estimation techniques that accommodate changing parameters. Challenges include greater analytical complexity and stability considerations, since changing dynamics can alter system behavior in nontrivial ways.