Let

y$($t$)=$ m$($t$)\backslash$sin$(2\backslash$pi f$\_$c t$)+\backslash$hat$\{$m$\}($t$)\backslash$cos$(2\backslash$pi f$\_$c t$),$

where f$\_$c is the carrier frequency, and m$($t$)=4\backslash$text$\{$sinc$\}(4$t$).$ Here, $\backslash$hat$\{$m$\}($t$)$ is the Hilbert transform of m$($t$).$

Please find Y$($f$)$ and determine whether y$($t$)$ is

$1.$ an upper$-$sideband AM signal, or

$2.$ a lower$-$sideband AM signal.

Please explain the reason.