Prevent Aliasing?

Question

What is the minimum sampaling rate (f_s) and sampling perios (T_s) that can be used to sample the signal without aliasing?

x(t)= cos(100*pi*t)

Answer 1

You need to sample at least twice the frequency of the signal, so if your frequency is 100 pi radians/sec, you would have to sample at 200 pi radians/sec.  In terms of Hz, your signal frequency is 50 Hz (w = 2 pi f = 100 pi), so you need to sample at 100 Hz or higher to avoid aliasing.