Linear Systems: Continuous-Time Impulse Response Descriptions

An important input–output description of a linear continuous-time system is its impulse response, which is the response h.t; / to an impulse applied at time . In time-invariant systems that are also causal and at rest at time zero, the impulse response is h.t; 0/ and its Laplace transform is the transfer function of the system. Expressions for h.t; / when the system is described by statevariable equations are also derived.