Split-radix FFT algorithm

About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.

An Implementation of Parallel 1-D FFT on the K Computer

Abstract: In this paper, we propose an implementation of a parallel one-dimensional fast Fourier transform (FFT) on the K computer. The proposed algorithm is based on the six-step FFT algorithm, which can be altered into the recursive six-step FFT algorithm to reduce the number of cache misses. The recursive six-step FFT algorithm improves performance by utilizing the cache memory effectively. We use the recursive six-step FFT algorithm to implement the parallel one-dimensional FFT algorithm. The performance results of one-dimensional FFTs on the K computer are reported. We successfully achieved a performance of over 18 TFlops on 8192 nodes of the K computer (82944 nodes, 128 GFlops/node, 10.6 PFlops peak performance) for a 2^41-point FFT.

On vectorizing the fast fourier transform

Abstract: A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm. The Stockham algorithm is then proposed for the entire computation of the two-dimensional fast Fourier transform on a vector computer.

Parallel system and method for performing fast fourier transform

Abstract: A parallel FFT generating system is disclosed for generating a Fast Fourier Transform (FFT) of an input vector. The parallel FFT generating system includes a plurality of processes configured to receive the input vector and process the input vector in parallel in relation to a set of twiddle factors to generate an output vector, the output vector comprising a Fourier transform representation of the input vector.

A new discrete Fourier transform algorithm using butterfly structure fast convolution

Abstract: This paper proposes a new approach to computing the discrete Fourier transform (DFT) with the power of 2 length using the butterfly structure number theoretic transform (NTT). An algorithm breaking down the DFT matrix into circular matrices with the power of 2 size is newly introduced. The fast circular convolution, which is implemented by the NTT based on the butterfly structure, can provide significant reductions in the number of computations, as well as a simple and regular structure, The proposed algorithm can be successively implemented following a simple flowchart using the reduced size submatrices. Multiplicative complexity is reduced to about 21 percent of that by the classical FFT algorithm, preserving almost the same number of additions.

Structured FFT and TFT: symmetric and lattice polynomials

Abstract: In this paper, we consider the problem of efficient computations with structured polynomials. We provide complexity results for computing Fourier Transform and Truncated Fourier Transform of symmetric polynomials, and for multiplying polynomials supported on a lattice.