DFT Efficient Computation on Digital Signal Processing related Questions and Answers

Question :   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)? 1. F1(k)+F2(k) 2. F1(k)- WNk F2(k) 3. F1(k)+WNkNk F2(k) 4. None of the mentioned Answer :   3 - F1(k)+WNkNk F2(k)