The output of any discrete time linear system is related to the input by the time-varying convolution sum: y [ n ] = ∑ ∑ m = − − ∞ ∞ n h [ n , m ] x [ m ] = ∑ ∑ m = − − ∞ ∞ ∞ ∞ h [ n , m ] x [ m ] or equivalently for a time-invariant system on redefining h, y [ n ] = ∑ ∑ k = 0 ∞ ∞ h [ k ] x [ n − − k ] = ∑ ∑ k = − − ∞ ∞ ∞ ∞ h [ k ] x [ n − − k ] where k = n − − m represents the lag time between the stimulus at time m and the response at time n.