Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

Dimensionless fast fourier transform method and apparatus

Abstract: A method and apparatus for calculating fast Fourier transforms FFTs are disclosed. An FFT of a given size is formatted using tensor product principles for implementation in apparatus or by software such that the same reconfigurable hardware or software can calculate FFTs of any dimension for the selected FFT size. The FFT is factored and presented to a first permutation block (10), then to first computation blocks (12, 14, 16, 18) for computing tensor products of dimensionless Fourier transforms of a relatively small base size and twiddle factors, then to a second permutation block (20), then to second computation blocks (22, 24, 26, 28), and finally to a third permutation block (30). The basic building blocks (10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30) of the circuitry can be reconfigurable for maximizing use-flexibility of the hardware or software.

Vectorization of fast fourier transform for elastic wave propogation for use in seismic underwater exploration of geographical areas of interest

Abstract: Numerical simulations of elastic wave propagation algorithms are critical components for seismic imaging and inversion. Finite-difference schemes yield good efficiency but cannot ensure the accuracy of the high frequency component. Pseudo-spectral algorithms are accurate up to the Nyquist frequency, but its efficiency depends on the optimization of the fast Fourier transform (FFT) algorithm. The conventional FFT algorithms are optimized for signal processing, in which problems are generally one dimensional time series. For 3D wave propagation, FFT algorithms have the potential to be further optimized. Under current computer hardware architecture, a vectorization scheme for high dimensional FFTs is presented. Compared to conventional numerical scheme implementations, the systems and methods disclose herein has the best performance on the slowest or higher dimensions of data. For elastic wave propagation, vectorization improves the efficiency by more than a factor of two when compared to standard FFT algorithms.

Tensor product algebra as a tool for VLSI implementation of the discrete Fourier transform

Abstract: A tool to aid in the automated VLSI implementation of the discrete Fourier transform (DFT) is described. This tool is tensor product algebra, a branch of finite-dimensional multilinear algebra. Tensor product formulations of fast fourier transform (FFT) algorithms to compute the DFT are presented. These mathematical formulations are manipulated, using properties of tensor product algebra, to obtain variants that adapt to performance constraints in a VLSI implementation process. The possibility of automating this procedure by processing these mathematical formulations or expressions in a behavioral synthesis environment of a silicon compilation system is discussed. A transformation technique between a symbolic computation environment and a behavioral synthesis environment for the transferring of functional primitives is discussed. >

The Cylindrical Taylor-Interpolation FFT Algorithm

Abstract: The cylindrical Taylor-interpolation FFT (TI-FFT) algorithm for the computation of the near-field and far-field in the "quasi-cylindrical" geometry has been developed. The cylindrical modal expansion of the vector potential is shown to be in the form that can make use of the cylindrical TI-FFT. The near-field on an arbitrary cylindrical surface is obtained from the vector potential and through the inverse FFT (IFFT). The far-field is obtained through the near-field far-field (NF-FF) transform. The cylindrical TI-FFT is valuable for back-scattering problems and "quasi-cylindrical" geometry. Like the planar TI-FFT algorithm, the cylindrical TI-FFT algorithm also has advantages of a N2 log2 N2 computational complexity, a low sampling rate, no basis functions and free of singularity problems.

Coded Fourier Transform

Abstract: We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a fraction of the inputs. We show that by exploiting the algebraic structure of the Fourier transform operation and leveraging concepts from coding theory, one can efficiently deal with the straggler effects. In particular, we propose a computation strategy, named as coded FFT, which achieves the optimal recovery threshold, defined as the minimum number of workers that the master node needs to wait for in order to compute the output. This is the first code that achieves the optimum robustness in terms of tolerating stragglers or failures for computing Fourier transforms. Furthermore, the reconstruction process for coded FFT can be mapped to MDS decoding, which can be solved efficiently. Moreover, we extend coded FFT to settings including computing general $n$-dimensional Fourier transforms, and provide the optimal computing strategy for those settings.