Radix-4 modular pipeline fast Fourier transform algorithm

摘要

In this work, we describe the design and implementation of the Radix-4 Modular Pipeline FFT. The Modular Pipeline algorithm differs from the Conventional FFT in terms of the storage of center elements to reduce the computation requirements without significant change in performance. We present a comparison between the Conventional FFT and Radix-4 Modular Pipeline FFT implementations, in terms of the number of computations, latency and hardware utilization, which are substantiated by our implementations using Xilinx Virtex 5, Virtex 6 devices and Quartus Stratix IV, Stratix V devices. As the size of FFT increases from 16 to 1024 points, the number of multiplications required increases from 12.5% to 25%. The estimated delay to compute the modular algorithm is improved by 24.08% for our implementation when compared to a conventional FFT. The Radix-4 Modular Pipeline implementation shows about twice the hardware utilization compared to the conventional FFT implementation.