Typically, Nyquist sampling, where Fs = 2B, is sufficient unless X(ω) contains impulses (or its derivatives) at the highest frequency B. Show that x(t) = cos(2πBt), which contains impulses at...

Typically, Nyquist sampling, where Fs = 2B, is sufficient unless X(ω) contains impulses (or its derivatives) at the highest frequency B. Show that x(t) = cos(2πBt), which contains impulses at frequency B, is an exception and can be recovered exactly using Nyquist sampling. Further, show that the signal x(t) = sin(2πBt) is completely lost when it is Nyquist sampled. What happens if x(t) = cos(2πBt + φ)?