$($a$)$

$($b$)$

$3.$ Sinusoidal Amplitude Modulation

In the following figure $(2$a$),$ a system is shown with the input signal $x(t)$ and the output signal $y(t).$ The "blocks" denote LTI systems with the indicated frequency response. The input signal has the Fourier transform $x(j)$ shown in Figure $2($b$).$

$($ii$)$ Determine and sketch $F(j),$ the output of the band$-$pass filter.