Suppose that a discrete-time signal x[n] is given by the formula
x[n] = 10 cos(0.2πn – π/7)
and that it was obtained by sampling a continuous-time signal at a sampling rate of fs = 1000 samples/sec.
(a) Determine two different continuous-time signals x1(t) and x2(t) whose samples are equal to x[n]; i.e., find x1(t) and x2(t) such that x[n] =x1(nTs) = x2 (nTs) if Ts = 0.001. Both of these signals should have a frequency less than 1000 Hz. Give a formula for each signal.
(b) If x[n] is given by the equation above, what signal will be reconstructed by an ideal D-to-C converter operating at sampling rate of 2000 samples/sec? That is, what is the output y(t) in Fig. 4-26 if x[n] is as given above?
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