Graph the signal x[n] formed by sampling the signal x(t) = 10 sin(8πt) at twice the Nyquist rate and x(t) itself. Then on the same graph at least two other continuous-time sinusoids which would yield exactly the same samples if sampled at the same times. A cosine x(t) and a sine signal y(t) of the same frequency are added to form a composite signal z(t). The signal z(t) is then sampled at exactly its Nyquist rate with the usual assumption that a sample occurs at time t = 0. Which of the two signals x(t) or y(t) would, if sampled by itself, produce exactly the same set of samples?
