The time-varying impulse response h (t 2, t 1) of a linear system is defined as the response of the system at time t = t 2 to a single impulse applied at time t = t 1. In other words, if the input x (t) to a linear system is x ( t ) = δ δ ( t − − t 1 ) where δ(t) represents the Dirac delta function, and the corresponding response y (t) of the system is y ( t = t 2 ) = h ( t 2 , t 1 ) then the function h (t 2, t 1) is the time-varying impulse response of the system. Since the system cannot respond before the input is applied the following causality condition must be satisfied: h ( t 2 , t 1 ) = 0 , t 2 < t 1