This problem is on the Matched Filter. Let's consider the simple signal s$($t$)$ whose Fourier transform S$($f$)$ is defined below:

S$($f$)=1,-$B $$ f $$ B$,$ where f in $[$Hz$]0,$ Otherwise

$($a$)$ Find s$($t$)$ using inverse Fourier Transform $($i$.$e$.,$ s$($t$)=$S$($f$)$e$^$j$2$ft df$)$ in the form of Sinc$($x$)=$sinx$/$x$.(3)$

$($b$)$ Assume this signal s$($t$)$ is given to the matched filter whose impulse response is h$($t$)=5$s$($T$-$t$).$ Calculate its output So$($f$)($frequency domain$)$ and so$($t$)($time domain$)$