(Solved): Problem 1: Let the LTI system described by the frequency response H(). Let us consider the input ...

Problem 1: Let the LTI system described by the frequency response $H(?)$. Let us consider the input $x(t)=3\cos (2t)+2\sin (10t)$ to this system $x(t)=3\cos (2t)+2\sin (10t)?\mathrm{H}(?)?y(t)$ A) Compute the output $y(t)$ in each of the following cases: 1) $H(?)=\frac{1}{2+j?}$. 2) $H(?)=\{\begin{array}{ll}1;& ?5???5\\ 0;& \text{ Otherwise }\end{array}$. B) Plot the input $x(t)$ and the corresponding output $y(t)$ in the same plot, for each system. C) compute the impulse response of each system.