Let x(t) be a signal whose Fourier transform X(ω) is nonzero only over 3 ≤ |ω| ≤ 9. Further, only frequencies 5 ≤ |ω| ≤ 7 contain useful information (the other frequencies can be considered to contain...

Let x(t) be a signal whose Fourier transform X(ω) is nonzero only over 3 ≤ |ω| ≤ 9. Further, only frequencies 5 ≤ |ω| ≤ 7 contain useful information (the other frequencies can be considered to contain noise or different channel information).

(a) What is the smallest sampling rate that will enable exact reconstruction of the useful signal if we do not perform any filtering on x(t) before sampling?

(b) How will the answer of part (a) change if it is permitted to pass x(t) through a filter before sampling? Explain.