A performance-efficient and datapath-regular implementation of modified split-radix fast Fourier transform

Discrete Fourier transform (DFT) finds various applications in signal processing, image processing, artificial intelligent, and fuzzy logic etc. DFT is often computed efficiently with Fast Fourier transform (FFT). The modified split radix FFT (MSRFFT) algorithm implements a length-N=2 DFT achieving a reduction of arithmetic complexity compared to split-radix FFT (SRFFT). In this paper, a simplified algorithm is proposed for the MSRFFT algorithm, reducing the number of real coefficients evaluated from 5/8N − 2 to 15/32N − 2 and the number of groups of decomposition from 4 to 3. A implementation approach is also presented. The approach makes data-path of the MSRFFT regular similar to that of the radix-2 FFT algorithm. The experimental results show that (1) MSRFFT consumes less time on central processing units (CPUs) with sufficient cache than existing algorithms; (2) the proposed implementation method can save execution time on CPUs and general processing units (GPUs).