Linear System - Time-varying Impulse Response

The time-varying impulse response h(t2,t1) of a linear system is defined as the response of the system at time t = t2 to a single impulse applied at time t = t1. In other words, if the input x(t) to a linear system is

where δ(t) represents the Dirac delta function, and the corresponding response y(t) of the system is

then the function h(t2,t1) is the time-varying impulse response of the system.

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