Problem $2$

The impulse response of an LTI is given by

$h(t)=\frac{sin(\frac{t}{2})sin(t)}{t^2}$

$($i$)$ Find the frequency response $H(j)$ for $h(t).($Note: Express $h_1(t)$ in Problem $1$ in terms of $h(t)$ and use your result from Problem $1).$

$($ii$)$ Plot the magnitude $|H(j)|.$

$($iii$)$ Let $m(t)$ be a periodic square wave signal with period $T=4$ shown below. Find the output $y(t)=m(t)**h(t).$

$($iv$)$ Let $g(t)=h(t)cos(t),$ use the multiplication property to find and sketch $G(j).$

$($V$)$ Find the output $y_2(t)=m(t)**g(t)$