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.

The fast Fourier transform algorithm for the production of the permutation factor circulant matrices

Abstract: A fast Fourier transform algorithm for the production of the permutation factor circulant matrices of order n based on the fast Fourier transform(FFT) was presented, and arithmetric complexity is O(nlog_2n).

FFT algorithms for prime transform sizes and their implementations on VAX, IBM3090VF, and IBM RS/6000

Abstract: Variants of the Winograd fast Fourier transform (FFT) algorithm for prime transform size that offer options as to operational counts and arithmetic balance are derived. Their implementations on VAX, IBM 3090 VF, and IBM RS/6000 are discussed. For processors that perform floating-point addition, floating-point multiplication, and floating-point multiply-add with the same time delay, variants of the FFT algorithm have been designed such that all floating-point multiplications can be overlapped by using multiply-add. The use of a tensor product formulation, throughout, gives a means for producing variants of algorithms matching computer architectures. >

A concurrent implementation of the prime factor algorithm on hypercube

Abstract: The prime factor algorithm (PFA) is an efficient discrete Fourier transform (DFT) computation algorithm in which a one-dimensional DFT is tuned into a multidimensional DFT, consisting of a few short DFTs whose lengths are mutually prime, and then an efficient algorithm is used for the short DFTs. The PFA was implemented on a hypercube using CrOS III communication routines, taking 120 ms to compute the DFT of 5040 complex points using 32 nodes of the Caltech-JPL MARK III Hypercube. It took 105 ms to do a DFT of 4096 complex points using the Cooley-Tukey algorithm with the same hardware configuration. The performance of hypercubes MARK III, NCUBE, and iPSC and the relative importance of communication and calculation are analyzed. With the current communication speed the Cooley-Tukey algorithm performs fast on a massively concurrent processor and the PFA is advantageous when the number of processors is less than 64 or so. The experience with using the PFA also serves as a useful guide to a multidimensional fast Fourier transform implementation using any algorithm. >

Area-efficient memory-based architecture for FFT processing

Abstract: In this paper, we propose a new area-efficient parallel architecture to calculate 2/sup n/-point FFT. The proposed architecture is based on the radix-4 Cooley-Tukey algorithm, and consists of four complex multipliers, eight complex adders, and four RAMs each of which is partitioned into two banks. The implemented FFT processor can calculate 2 K/4 K/8 K-point complex FFT in 28.2 /spl mu/s/62.0 /spl mu/s/135.2 /spl mu/s at 91 MHz, respectively.

A new fast algorithm for calculating near-field propagation between arbitrary smooth surfaces

Abstract: A new fast algorithm using multilevel Taylor interpolation and the FFT (TI-FFT) has been developed to solve the near-field (NF) propagation problem for the planar scenario. The algorithm speeds the computation by grouping neighborhood regions in the spatial domain or the spectral domain through the Taylor interpolation (TI) method using the FFT technique. The CPU time increases as O(N/sup 2/ log/sub 2/ N/sup 2/) instead of the polynomial time O(N/sup 4/) required for the Stratton-Chu formula for N /spl times/ N observation points. The multilevel TI-FFT uses a sampling rate above the Nyquist rate as required by the FFT, while the Stratton-Chu formula requires a higher sampling rate because of the fast variation of the phase term. An accuracy of -50 dB for the multilevel TI-FFT algorithm is easily obtained and an accuracy of -70 dB is possible when the algorithm is optimized. The algorithm works particularly well for band-limited beam-like fields and "quasi-planar" surfaces.