If we split the N point data sequence into two N/2 point data sequences f1(n) and f2(n) corresponding to the even numbered and odd numbered samples of x(n) and F1(k) and F2(k) are the N/2 point DFTs of f1(k) and f2(k) respectively, then what is the N/2 point DFT X(k) of x(n)?
A. F1(k)+F2(k)
B. F1(k)- WNk F2(k)
C. F1(k)+WNkNk F2(k)
D. None of the mentioned
Answer:A
If we split the N point data sequence into two N/2 point data sequences f1(n) and f2(n) corresponding to the even numbered and odd numbered samples of x(n) and F1(k) and F2(k) are the N/2 point DFTs of f1(k) and f2(k) respectively, then what is the N/2 point DFT X(k) of x(n)?
A. F1(k)+F2(k) B. F1(k)- WNk F2(k) C. F1(k)+WNkNk F2(k) D. None of the mentioned
Explanation: From the question, it is given that