Problem $1$

Let $x_1(t)=\frac{sin(\frac{t}{2})}{t}$ and $x_2(t)=\frac{sin(t)}{t}$ two continuous time signals, $x_1(j)$ and $x_2(j)$ their respective Fourier transform given graphically below. Let $h_1(t)=x_1(t)x_2(t),$ the product of $x_1(t)$ and $x_2(t).$

$($a$)$ Determine the Fourier transform $H_1(j)$

$($b$)$ Sketch the magnitude $|H_1(j)|$

Figure $2$: $x_2(j)$