Consider a real finite-length sequence x[n] with Fourier transform X(e j ) and DFT X[k]. If Jm{X[k]} = 0, k= 0,1,., N 1. Can

Consider a real finite-length sequence x[n] with Fourier transform X(e^jω) and DFT X[k]. If 

Jm{X[k]} = 0,             k= 0,1,…., N – 1.

 Can we conclude that 

Jm{X(e^jω)} = 0,            − π ≤ ω ≤ π?

State your reasoning if your answer is yes. Give a counterexample if your answer is no.