Suppose we have a causal LTI system with rational system function H(s). We don't know H(s), but we do have the following information:
i. When the input to the system is x(t) = u(t), the output y(t) is absolutely integrable.
ii. When the input to the system is x(t) = tu(t), the output y(t) is not absolutely integrable.
iii. H(1) = 3.
iv. The signal r(t), given below, is of finite length.
r(t) = d^h/dt^2+ 2(dh/dt)+ 2h(t)
v. H(s) has exactly one zero at f.
Determine H(s) as precisely as you can.