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.

A modified discrete fourier transform algorithm: A delta rotation algorithm

Abstract: A new method for the evaluation of the Discrete Fourier Transform (DFT) is presented. This method evaluates the DFT of samples of a continuous time signal by multiplying the DFT of the difference signal at the output of a Linear Delta Modulator (LDM) by a rotation factor. The novelty of the proposed algorithm is to reduce the number of multiplication and to simplify the hardware implementation. Further modification of this algorithm does not require any multiplication at all during the DFT computation. An implementation of convolutions, chirp-z transform and the discrete Hilbert transform with the proposed technique will offer good opportunities for additional research with respect to the point of a simple hardware implementation, high-speed, and a computational simplicity. This proposed technique is, in fact, the combination of an encoding technique and a FFT algorithm. The results show a very promising and will be a viable alternative to the FFT and any other DFT algorithms.

Group Invariant Fourier Transform Algorinthms1

Abstract: Publisher Summary The design of algorithms for computing the crystallographic Fourier transform is a subject in applied group theory. This chapter presents a discussion on group invariant Fourier transform algorithms. Finite abelian groups serve as data indexing sets. A class of affine group fast Fourier transform (FFT) algorithms is introduced, which fully use data invariance with respect to subgroups of the affine group of data indexing sets. The chapter reviews all the necessary group theory. The affine group of a finite abelian group is defined. Constructs related to the action of affine subgroups on data indexing sets are introduced in the chapter. The chapter defines the Fourier transform of an abelian group and discussed its fundamental role in interchanging periodization and decimation operations (duality). The reduced transform (RT), Cooley–Tukey algorithm (CT), FFT, and Good–Thomas (GT) algorithms are presented as applications of this duality to different global decomposition strategies. Affine group FFT algorithms based on the RT algorithm are discussed, while those coming from the application of the affine group CT, FFT are introduced. The chapter describes a method of incorporating one-dimensional (1D) symmetry into FFT computations, which calls on lower order existing FFT routines using the symmetry condition. The chapter presents many examples to reflect both the theory and experience and others, over several years in writing code for the three-dimensional (3D) crystallographic FT.

High-Performance Scalable Base-4 Fast Fourier Transform Mapping

Abstract: : This paper describes a novel, scalable, parallel Fast Fourier Transform (FFT) architecture mapping that supports transform lengths that are not powers of two or four, that provides low latency as well as high throughput, that can do both 1-D and 2-D Discreet Fourier Transforms (DFTs), that is ideally suited to today's complex FPGA architectures, that possesses all the regularity and design simplicity of systolic arrays, and that is naturally suited to a parameterized HDL form. Its algorithmic underpinnings are based on an observation that with suitable permutations, the DFT coefficient matrix can be partitioned into regular blocks of smaller "base-4" matrices (equivalent to a decimation in time and frequency). From this new base-4 matrix DFT description the authors have derived a new latency and throughput optimal base-4 FFT architecture. It combines the performance of traditional radix-4 "pipelined FFTs" with the design and implementation simplicity of systolic arrays, and yet is versatile. Twenty-six briefing charts summarize the presentation.

Improved arithmetic Fourier transform algorithm

Abstract: A new improved version of the arithmetic Fourier transform algorithm is presented. This algorithm computes the Fourier coefficients of continuous -time signals using the number-theoretic technique ofMobius inversion. The major advantage of this algorithm is that it needs mostly addition operations, except for a few real multiplications. The improved version can be realized efficiently on integrated circuit chips and optical parallel processors using tapped delay lines.

Fast Fourier Transforms in Electromagnetics

Abstract: This Chapter review the fast Fourier transform (FFT) technique and its application to computational electromagnetics, especially to the fast solver algorithms including the Conjugate Gradient Fast Fourier Transform (CG-FFT) method, Precorrected Fast Fourier Transform (pFFT) method, Adaptive Integral Method (AIM), Greens Function Interpolation with FFT (GI-FFT) method and Integral Equations with FFT (IE-FFT) method. The basic ideas used in the FFT applications are addressed while the brief introduction to integral equation method is conducted. The general formulation and procedure in the integral equation method, surface integral equations, volume integral equations, solutions to integral equations, and their implementations of fast Fourier transform algorithm are also briefed together with fast convolution using fast Fourier transform. Fast integral equation method developed based on fast Fourier transform are reviewed where conjugate gradient fast Fourier transform method, and precorrected fast Fourier transform method (where projection operators and interpolation operators are also highlighted), adaptive integral method, Greens function interpolation with FFT approach and integral equations with FFT method are also described. While the matching schemes for gradients of Green's functions are addressed, accuracy and complexity, memory requirement and computational cost, and error controls and estimations are also discussed. Keywords: Electromagnetics; Antennas; Scattering; Fourier transform; Numerical Analysis