Signals and Systems

Many continuous processes or phenomena that one might wish to study or model take the form of linear time-invariant input-output systems. Examples include analog electronic circuits, wave phenomena, electromagnetism, optics, and major classes of physical and mathematical systems. These may be represented by a time-varying input s(t), a characteristic and stable ``system function" h(t) describing the properties of the system or medium, and a time-varying output response r(t) from the system:

$s(t) \longrightarrow \; \;$ $\; \; \longrightarrow r(t)$

The study of such systems is called linear systems analysis, and it represents one of the key (and most exhaustively understood) areas of continuous mathematics. The next several sections describe the analysis of such systems.