The DFT of a vector [a b c d] is the vector [α β γ δ ]. Consider the product The DFT of the vector [ p q r s] is a scaled version of

Two system with impulse responses h₁(t) and h₂(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is

The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of the step response at t = 2 is