Lineaire tijdsinvariante systemen

A system is linear if it displays the characteristics of homogeneity and additivity, together termed as the superposition property, a principle observed in all linear systems.

Linear time-invariant systems, LTI, are systems where the principles of linearity and time invariance apply.

The input-output behavior of an LTI system can be fully defined by observing its response to an impulsive excitation at its input. Once this response is known, the system's reaction to any other input can be calculated using convolution.

Linear systems are often represented by linear differential equations, where coefficients may or may not be functions of time.

If the coefficients are time-invariant, the system it represents becomes a linear, constant coefficient differential equation often referred to as LCCDE.

LCCDEs typically model electrical circuits with ideal components and single or even multiple independent sources using the superposition principle.

An LTI system can modify the amplitude and phase of an input sinusoid or complex exponential signal without changing its frequency, making it an essential tool for designing systems to filter noisy signals and images.