A note on sampling the sinusoidal signal with Nyquist rate

Discussion on sampling the sinusoidal signal with Nyquist rate is presented. Let f(t)= A sin(2π f 0 t+φ) be the general form of sinusoidal signal, and f(nT s)= A sin(2π f 0 nT s+φ) the uniformly sampling of f(t) with Nyquist rate of f s= 2f 0 (i.e. the sampling space T s= 1/f s= 1/2f 0 ). It is generally considered that the sequence f(nT s) contains all the information about f(t),and that, at least, within certain constraints, f(t) can be uniquely reconstructed from f(nT s). However, from the view of point of frequency overlap, sampling the sinusoidal signal with Nyquist rate violates the demand of the sampling theorem. A thorough analysis of this problem in frequency domain is presented, and a correction of the aforementioned conclusion is given.