Linear systems

A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.

A general deterministic system can be described by an operator, ${\displaystyle H}$, that maps an input, ${\displaystyle x(t)}$, as a function of ${\displaystyle t}$ to an output, ${\displaystyle y(t)}$, a type of black box description. Linear systems satisfy the property of superposition. Given two valid inputs

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