Question 1
Given the transfer function H(s)=$\frac{9}{s^{2}+6s+9}$ for a causal LTI system, what is the impulse response h(t)?
Question 2
An LTI system has impulse response h(t)=e^{-2t}u(t) and input x(t)=t\,u(t). What is the output y(t)=x(t)*h(t)?
Question 3
Given X(s)=$\frac{5(s+1)}{s(s+2)}$ for a causal signal x(t), what are x(0+) and $\lim_{t\to\infty}$x(t)?
Question 4
For f(t)=e^{2t}u(t)-3e^{-t}u(t), what is F(s) and its region of convergence?
Question 5
For the transfer function H(s)=$\frac{s+5}{s^{2}+4s+5}$, identify its zero, poles, and determine BIBO stability.
