A Reduced-Complexity Fast Algorithm for Software Implementation of the IFFT/FFT in DMT Systems

The discrete multitone (DMT) modulation/demodulation scheme is the standard transmission technique in the application of asymmetric digital subscriber lines (ADSL) and very-high-speed digital subscriber lines (VDSL). Although the DMT can achieve higher data rate compared with other modulation/demodulation schemes, its computational complexity is too high for costefficient implementations. For example, it requires 512-point IFFT/FFT as the modulation/demodulation kernel in the ADSL systems and even higher in the VDSL systems. The large block size results in heavy computational load in running programmable digital signal processors (DSPs). In this paper, we derive computationally efficient fast algorithm for the IFFT/FFT. The proposed algorithm can avoid complex-domain operations that are inevitable in conventional IFFT/FFT computation. The resulting software function requires less computational complexity. We show that it acquires only 17% number of multiplications to compute the IFFT and FFT compared with the Cooly-Tukey algorithm. Hence, the proposed fast algorithm is very suitable for firmware development in reducing the MIPS count in programmable DSPs.