Problem $2-$ Sampling Theory $[22$ pts$]$

The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is

called the Nyquist rate. Determine the Nyquist rate corresponding to the following signal:

x$($t$)=($sin$(4000\backslash$pi t$))/(\backslash$pi t$)$

Let x$($t$)$ be a signal with Nyquist rate $\backslash$omega $\_(0).$ Determine the Nyquist rate for the signal x$^(2)($t$).$