$($Under$-$sampling and aliasing$)$ The sampling theorem says that if $1)$ the input signal x$($t$)$ is band$-$limited to wm; and $2)$ the sampling rate ws $=2$pi$/$T $>2$wm$,$ then the reconstructed signal x$($t$)$ from the ideal low pass filter is equal to the originial continuous$-$time signal x$($t$)$ for all t