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If X(k) is the N/2 point DFT of the sequence x(n), then what is the value of X(k+N/2)?

If X(k) is the N/2 point DFT of the sequence x(n), then what is the value of X(k+N/2)? Correct Answer F1(k)-WNk F2(k)

We know that, X(k) = F1(k)+WNk F2(k) We know that F1(k) and F2(k) are periodic, with period N/2, we have F1(k+N/2) = F1(k) and F2(k+N/2)= F2(k). In addition, the factor WNk+N/2 = -WNk. Thus we get, X(k+N/2)= F1(k)- WNk F2(k).

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