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

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

A low–pass filter with a cut-off frequency of 30 Hz is cascaded with a high-pass filter with a cut-off frequency of 20 Hz. The resultant system of filters will function as

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