$5\mathrm{.}1-4$ Two signals $g_1(t)=1000(4000t)$ and $g_2(t)=2000(8000t)$ are applied at the inputs of ideal LPFs $H_1(f)=(\frac{f}{8},000)$ and $H_2(f)=(\frac{f}{5},000)($Fig$.$ P$5\mathrm{.}1-4).$ The outputs $y_1(t)$ and $y_2(t)$ of these filters are multiplied to obtain the signal $y(t)=y_1(t)y_2(t).$ Find the Nyquist rate of $y_1(t),y_2(t),$ and $y(t).$ Use the convolution property and the width property of convolution to determine the bandwidth of $y_1(t)y_2(t).$

P$5\mathrm{.}1-4$