GATE EC 2014 Q55: Find x for DFT(DFT(x))=x (N=4)

EC > GATE 2014 SET-4 > DFT

The N-point DFT X of a sequence x[n], 0 ≤ n ≤ N − 1 is given by

Denote this relation as X = DFT(x). For N = 4, which one of the following sequences satisfies DFT(DFT(x)) = x?

x = [1 2 3 4]

x = [1 2 3 2]

x = [1 3 2 2]

x = [1 2 2 3]

Correct : b

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