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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.
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TL;DR: The CG-NUFFT method can solve the integral equation with both uniform and nonuniform grid while retaining the efficiency of the CG-FFT method, and results demonstrate that they can solve much larger problems than the MoM.
Abstract: This paper presents the application of the conjugate-gradient (CG) fast Fourier transform (FFT) (CG-FFT) method and the CG nonuniform FFT (CG-NUFFT) method for the integral equation arising from acoustic scattering problems. In the conventional method of moments (MoM) for integral equations, the CPU and memory requirements are O(N/sup 3/) and O(N/sup 2/), respectively, where N is the number of unknowns in the problem. The CG-FFT method, which combines the iterative conjugate-gradient method with FFT, reduces these requirements to O(KN log/sub 2/N) and O(N), respectively, where K is the number of CG iterations. The CG-NUFFT method differs from the CG-FFT method in that it makes use of nonuniform FFT algorithms instead of FFT to allow a nonuniform discretization. Therefore, the CG-NUFFT method can solve the integral equation with both uniform and nonuniform grid while retaining the efficiency of the CG-FFT method. These two methods are applied to solve for two-dimensional constant density acoustic scattering problems. Numerical. results demonstrate that they can solve much larger problems than the MoM.
20 citations
TL;DR: A generalization of the sliding FFT, which introduces a wide class of orthogonal transforms that can be implemented with the order of N complexity is proposed.
Abstract: Implementation of the transform domain adaptive filters is addressed. Recent results have shown that if the input data to a radix-2 fast Fourier transform (FFT) structure is sliding one sample at a time, only N-1 butterflies need to be calculated for updating the FFT structure. This is opposed to most of the previous reports that assume order of NlogN complexity for such implementation. In this correspondence, a generalization of the sliding FFT, which introduces a wide class of orthogonal transforms that can be implemented with the order of N complexity is proposed. >
20 citations
19 Jun 2005
TL;DR: Results show that the design and hardware implementation of a FFT-based algorithm using modular arithmetic to efficiently compute very large number multiplications starts to be useful for 4096-bit operands and beyond.
Abstract: Modular multiplication (MM) for large integers is the foundation of most public-key cryptosystems, specifically RSA, El-Gamal and the elliptic curve cryptosystems. Thus MM algorithms have been studied widely and extensively. Most of works are based on the well known Montgomery multiplication method (MMM) and its variants, which require multiplication in N. Authors have always avoided the fast Fourier transform (FFT) method believing that it is impractical for present system sizes despite its smaller complexity order. In this paper, the authors presented the design and hardware implementation of a FFT-based algorithm using modular arithmetic to efficiently compute very large number multiplications. The algorithm has been implemented in CASM, an intermediate level HDL developed in the laboratory. The target architecture is a FPGA. The algorithm is scalable and can easily be mapped to any operand size. Results show that such algorithm implementation starts to be useful for 4096-bit operands and beyond.
20 citations
TL;DR: In this article, an efficient FFT algorithm is developed for discontinuous functions with both uniform and non-uniform sampled data, with O(Np+N log n) complexity, where N is the number of sampling points and p is the interpolation order.
Abstract: In the conjugate gradient–fast Fourier transform (CGFFT) method, the FFT is used to evaluate the convolution integrals. When the function to be transformed has discontinuities, the accuracy of the FFT results, and thus the CGFFT results, will degrade. In this letter, an efficient FFT algorithm is developed for discontinuous functions with both uniform and nonuniform sampled data, with O(Np+N log N) complexity, where N is the number of sampling points and p is the interpolation order. The algorithm is incorporated into the CGFFT method. Numerical results for slabs demonstrate the efficiency and accuracy of the new FFT and CGFFT algorithms. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 47–49, 2001.
20 citations
01 Jan 1988
TL;DR: The implementation on the CRAY-1 of a prime factor FFT algorithm which adapts some of these developments to a vector-processing scientific computer and it is shown that worthwhile gains are obtained in both speed and storage requiremennts.
Abstract: Recent developments in algorithm design have made the Fast Fourier Transform even faster. We described the implementation on the CRAY-1 of a prime factor FFT algorithm which adapts some of these developments to a vector-processing scientific computer. Comparative times are given for the new and old versions of the FFT algorithm, applied to the problem of performing multiple simultaneous complex transforms. It is shown that worthwhile gains are obtained in both speed and storage requiremennts. The new algorithm is also vectorizable in the more difficult cases of a single transform. Finally, we use timing measurements of the new routine to estimate the value on the CRAY-1 of Hockney's parameter n 1 2 , which characterizes a computer in terms of its apparent degree of parallelism.
20 citations