Two systems 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) = tu(t). For an input u(t − 1), the output is

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is

Given two continuous time signals $$x\left(t\right)=e^{-t}$$ and $$y\left(t\right)=e^{-2t}$$ which exist for t > 0, the convolution z(t) = x(t)*y(t) is