Balanced Binary-Tree Decomposition for Area-Efficient Pipelined FFT Processing

摘要

This paper presents an area-efficient algorithm for the pipelined processing of fast Fourier transform (FFT). The proposed algorithm is to decompose a discrete Fourier transform (DFT) into two balanced sub-DFTs in order to minimize the total number of twiddle factors to be stored into tables. The radix in the proposed decomposition is adaptively changed according to the remaining transform length to make the transform lengths of sub-DFTs resulting from the decomposition as close as possible. An 8192-point pipelined FFT processor designed for digital video broadcasting—terrestrial (DVB-T) systems saves 33% of general multipliers and 23% of the total size of twiddle factor tables compared to a conventional pipelined FFT processor based on the radix-$2^{2}$ algorithm. In addition to the decomposition, several implementation techniques are proposed to reduce area, such as a simple index generator of twiddle factor and add/subtract units combined with the two's complement operation.