# 45. The N-point DFT X of a sequence x [n] ,0≤ ...

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

$X[k]={1\over \sqrt N}\Sigma^{N-1}_{n=0}x[n]e^{-j{2\pi \over N}nk}$   0 ≤ k ≤ N - L

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

(A) x=[1 2 3 4]

(B) x=[1 2 3 2]

(C) x=[1 3 2 2]

(D) x=[1 2 2 3]

Hint:
Explanation:

Discuss the solution.