3.4-3 Signals $g_1(t) = 10^3e^{-1000t}u(t)$ and $g_2(t) = \delta(t - 100)$ are applied at the inputs of the ideal lowpass filters $H_1(f) = \Pi(f/2000)$ and $H_2(f) = \Pi(f/1000)$ (Fig. P3.4-3). The outputs $y_1(t)$ and $y_2(t)$ of these filters are multiplied to obtain the signal $y(t) = y_1(t)y_2(t)$.
(a) Sketch $G_1(f)$ and $G_2(f)$.
(b) Sketch $H_1(f)$ and $H_2(f)$.
(c) Sketch $Y_1(f)$ and $Y_2(f)$.
(d) Find the bandwidths of $y_1(t)$, $y_2(t)$, and $y(t)$.
