Split-Radix FFT Algorithms Based on Ternary Tree

Fast Fourier Transform (FFT) is widely used in signal processing applications. For a 2n-point FFT, split-radix FFT costs less mathematical operations than many state-of-the-art algorithms. Most split-radix FFT algorithms are implemented in a recursive way which brings much extra overhead of systems. In this paper, we propose an algorithm of split-radix FFT that can eliminate the system overhead. Ternary tree schedule algorithms for split-radix FFT will be introduced. Additionally, we use some optimizing technologies such as loop unrolling, data prefetching and instruction pipeline adjustment to enhance performance. For large size split-radix FFT, we propose an efficient algorithm that uses "BFS+BFS" traversal model in the ternary tree to reduce the overhead of memory access. In the end, experimental results on Godson-3A2000 show that the algorithm in an iterative way performs 20% better than the algorithm in a recursive way. Compared with standard library FFTW3, the performance of the optimized algorithm in an iterative is promoted by 30%.