1. OFDM DFT  DFT  Inverse DFT  An N-point DFT (or inverse DFT) requires a total of N 2 complex multiplications  This transform can be implemented very efficiently by the fast Fourier transform (FFT)

2. OFDM OFDM implementation  An OFDM signal consists of a sum of subcarriers that are modulated by using QAM, and is implemented using the inverse DFT (discrete Fourier transform) di : the i-th complex QAM symbol N : the number of subcarriers

3. OFDM FFT  The FFT drastically reduces the amount of calculations by exploiting the regularity of the operations in the DFT  Using the radix-2 algorithm, an N-point FFT (or inverse FFT) requires only (N/2)log 2 N complex multiplications 256 multiplications for DFT versus 32 for FFT (for a 16-point transform) – a reduction by a factor of 8 In VDSL system, 4096-point transform is used – a reduction by a factor of about 683

4. Homework  16-point DFT & 16-point inverse DFT programming  16-point FFT & 16-point inverse FFT programming (Tip)  Definition for complex variable should be needed  Complex variable (real + imaginary, A=a+ib)  Complex multiplication (A*B=(a+ib)*(c+id)=(ac-bd)+i*(ad+bc))  Complex addition (A+B=(a+ib)+(c+id)=(a+c)+i*(b+d))  Complex subtraction (A-B=(a-c)+i*(b-d))  Block diagram  마감 : 12 월 12 일 수요일 낮 12 시까지 ( 교수 이메일로 보낼것 )  제출자료 source program (c-code) with comments.exe file (file_name = student_id.exe) for demonstration