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.

An OpenMP Parallelized Multilevel Green's Function Interpolation Method Accelerated by Fast Fourier Transform Technique

Abstract: A parallelized multilevel Green's function interpolation method (MLGFIM) accelerated by fast Fourier transform (FFT) technique is proposed The difficulties in applying various improved interpolation schemes to effectively reduce the number of interpolation points are overcome by using the FFT technique In order to accelerate the convergence property of the iterative solution using the proposed algorithm, a recently proposed preconditioning scheme, ie, multiplicative Calderon preconditioner is adopted to transform the first kind integral operator to the second kind, albeit an increase of computer memory storage requirement An OpenMP parallel implementation of the MLGFIM-FFT algorithm on a share-memory computer system is developed to analyze various electrically large electromagnetic scattering problems including a NASA almond, a 20-wavelength cylinder capped with two half spheres, and a 37-wavelength cylinder array Numerical results illustrate good computational performance of the proposed algorithm

Cyclic convolution of real sequences: Hartley versus Fourier and new schemes

Abstract: Recently, new fast transforms (such as the discrete Hartley transform in particular) have been proposed which are best suited for the computation of cyclic convolution of real sequences. Two approaches using Fourier or Hartley transforms are first compared, showing that the recently proposed FFT algorithms for real data present a lower arithmetic complexity than the corresponding DHT-based approach. Improvements are made to both types of algorithms, leading to different trade offs between arithmetic and structural complexity. We also present a new Hartley Transform algorithm with lower arithmetic complexity than any previously published one.

Efficient address generation for prime factor algorithms (digital signal processing)

Abstract: An attempt is made to explain as clearly as possible the problem of address generation and how the prime factor mapping technique is used in this class of algorithms. Two novel address generation schemes are proposed to improve efficiency. The first scheme reduces the computation required for unscrambling data in an in-place realization of the PFA (prime factor algorithm) by reducing the number of variables used to calculate the data addresses. The second scheme is to be used in an in-place in-order realization of PFA. It achieves high efficiency by replacing complicated modulo operations of conventional approaches by simple indirect addressing techniques. Making use of this scheme, software packages have been written for the computation of DFTs (discrete Fourier transforms) using a high-level language and two low-level languages (the 80286/287 and TMS330C25 assembly languages). Results of these realizations show that a reduction of 50% in address generation time is achievable, giving a saving of 30% in total computation time. A hardware address generator is also developed, which may provide clues to improving digital signal processor architectures in the future. >

Efficient implementation of large size FFT

Abstract: A system and method of implementing a Fast Fourier Transform (FFT) function in a high data rate communication network. The communication network, employing technology such as VDSL and DMT or FDM, frequently implements a FFT at a transmitter to transfer frequency domain modulated signals into time domain signals. An IFFT is implemented at the receiver to obtain the original signal. The present system divides the channel bandwidth into sub-bands and performs the FFT function with multiple FFTs in order to reduce chip size and computation time.

Fast Computation of Partial Fourier Transforms

Abstract: We introduce two ecient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reection seismology. In both algorithms, the main idea is to decompose the summation domain of into simpler components in a multiscale way. Existing fast algorithms are then applied to each component to obtain optimal complexity. The algorithm in 1D is exact and takes O(N log 2 N) steps. Our solution in 2D is an approximate but accurate algorithm that takes O(N 2 log 2 N) steps. In both cases, the complexities are almost linear in terms of the degree of freedom. We provide numerical results on several test examples.