A signal x (t) is sampled four times to produce the signal x [n] and the sample values are {x [0] , x [1] , x [2] , x [3] } = {7, 3, ? 4, a} .
This set of four numbers is the set of input data to the DFT which returns the set {X [0] , X [1] , X [2] , X [3] } .
(a) What numerical value of a makes X [?1] a purely real number?
(b) Let a = 9. What is the numerical value of X [29] ?
(c) If X[15] = 9 ? j2, what is the numerical value of X [1] ?
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