A bandlimited periodic signal x(t) whose highest frequency is 25 Hz is sampled at 100 samples/second over exactly one fundamental period to form the signal x[n]. The samples are {x[0], x[1], x[2], x[3]} = {a, b, c, d}.
(a) Let one period of the DFT of those samples be {X[0], X[1], X[2], X[3]}. What is the value of X[1] in terms of a, b, c, and d?
(b) What is the average value of x(t) in terms of a, b, c, and d?
(c) One of the numbers {X[0], X[1], X[2], X[3]} must be zero. Which one is it and why?
(d) Two of the numbers {X[0], X[1], X[2], X[3]} must be real numbers. Which ones are they and why?
(e) If X[1] = 2 + j3, what is the numerical value of X[3] and why?
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