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.

Method and system for bit stacked fast fourier transform

Abstract: An FFT algorithm that splits a large bit width waveform into two parts, making it possible to conduct the FFT with much lower logic resource consumption is disclosed. The waveform is split into its most significant bits and its least significant bits through division in the form of a bit shift. Each partial signal is then put through an FFT algorithm. The MSB FFT output is then right bit shifted. The two partial FFT's are summed to create a single output that is largely equivalent to an FFT of the original waveform. Rounding distortion is reduced by overlapping the MSB and LSB partial signals.

A fast and accurate numerical method for symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula

Abstract: In this paper, we propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar Levy processes. The method is based on the accurate numerical formulas for Fourier transform proposed by Ooura. These formulas are combined with nonuniform fast Fourier transform (FFT) and fractional FFT to speed up the numerical computations. Moreover, we propose a formula for numerical indefinite integration on equispaced grids as a component of the method. The proposed integration formula is based on the sinc-Gauss sampling formula, which is a function approximation formula. This integration formula is also combined with the FFT. Therefore, all steps of the proposed method are executed using the FFT and its variants. The proposed method allows us to be free from some special treatments for a non-smooth initial condition and numerical time integration. The numerical solutions obtained by the proposed method appeared to be exponentially convergent on the interval if the corresponding exact solutions do not have sharp cusps. Furthermore, the real computational times are approximately consistent with the theoretical estimates.

Symmetric prime factor fast fourier transform algorithms

Abstract: The prime factor algorithm (PFA) is a fast algorithm for the evaluation of the discrete Fourier transform (DFT), applicable when the sequence length N is a product of relative primes. PFAs are presented that take advantage of the symmetry in a real-even or real-odd sequence. These algorithms require only one-fourth the real arithmetic and storage requirements of the complex PFA. As with existing state-of-the-art PFAs, these algorithms can be performed in-place and in-order.

Fast discrete Fourier transform with exponentially spaced points

Abstract: The use of fast algorithms for evaluation of discrete Fourier transform-inverse transform pairs with uniformly spaced input data but with output data required only at exponentially spaced intervals is investigated. The algorithms require order (N) arithmetic operations, rather than the order (N log(N)) required for the full FFT algorithm.

An Algorithm for Computing DFT Using Arithmetic Fourier Transform

Abstract: The Discrete Fourier Transform (DFT) plays an important role in digital signal processing and many other fields.In this paper,a new Fourier analysis technique called the arithmetic Fourier transform (AFT) is used to compute DFT.This algorithm needs only O(N) multiplications.The process of the algorithm is simple and it has a unified formula,which overcomes the disadvantage of the traditional fast method that has a complex program containing too many subroutines.The algorithm can be easily performed in parallel,especially suitable for VLSI designing.For a DFT at a length that contains big prime factors,especially for a DFT at a prime length,it is faster than the traditional FFT method.The algorithm opens up a new approach for the fast computation of DFT.