c) The signals
$g_1(t) = 5 \cos(2\pi \cdot 15,000t) + 3 \cos(2\pi \cdot 25,000t)$
and
$g_2(t) = 2 \cos(2\pi 5,000t) + 4 \cos(2\pi \cdot 12,000t)$ are
applied at the input of the ideal lowpass filters
$H_1 = \Pi(\frac{f}{35,000})$ and $H_2 = \Pi(\frac{f}{12,000})$
as shown in Figure 1.
i) Sketch the spectra of $G_1(f)$ and $G_2(f)$ (2 point)
ii) Sketch the spectra of $H_1(f)$ and $H_2(f)$ (3 point)
iii) Sketch the spectra of $Y_1(f)$, $Y_2(f)$ and $Y(f)$ (5 point)
iv) Find the bandwidth of $y_1(t)$, $y_2(t)$ and $y(t)$ (5 point)
$y_1(t)$
$g_1(t)$
$H_1(t)$
$\times$
$y(t) = y_1(t)y_2(t)$
$y_2(t)$
$g_2(t)$
$H_2(t)$
Figure 1
