Topic
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.
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TL;DR: A statistical analysis of the transform domain displacement estimation algorithm and its convergence under certain realistic conditions is given and an extension of the algorithm that adaptively updates displacement estimation according to the local features of the moving objects is described.
Abstract: This paper introduces an algorithm for estimating the displacement of moving objects in a television scene from spatial transform coefficients of successive frames. The algorithm works recursively in such a way that the displacement estimates are updated from coefficient to coefficient. A promising application of this algorithm is in motion-compensated interframe hybrid transform- dpcm image coding. We give a statistical analysis of the transform domain displacement estimation algorithm and prove its convergence under certain realistic conditions. An analytical derivation is presented that gives sufficient conditions for the rate of convergence of the algorithm to be independent of the transform type. This result is supported by a number of simulation examples using Hadamard, Haar, and Slant transforms. We also describe an extension of the algorithm that adaptively updates displacement estimation according to the local features of the moving objects. Simulation results demonstrate that the adaptive displacement estimation algorithm has good convergence properties in estimating displacement even for very noisy images.
37 citations
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TL;DR: It is shown that prime factor FFT algorithms offer little improvement over conventional F FT algorithms on computers such as the Cray-1 and Cyber 205 where the multiplications can be performed in parallel with the additions.
37 citations
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TL;DR: In this article, a fast butterfly algorithm for the hyperbolic Radon transform is proposed, which reformulates the transform as an oscillatory integral operator and constructs a blockwise low-rank approximation of the kernel function.
Abstract: Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N2 log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration.
37 citations
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13 Sep 2009TL;DR: It is shown that a two-dimensional decomposition effectively improves performance by reducing the communication time for larger numbers of MPI processes.
Abstract: In this paper, we propose an implementation of a parallel three-dimensional fast Fourier transform (FFT) with two-dimensional decomposition on a massively parallel cluster of multi-core processors. The proposed parallel three-dimensional FFT algorithm is based on the multicolumn FFT algorithm. We show that a two-dimensional decomposition effectively improves performance by reducing the communication time for larger numbers of MPI processes. We successfully achieved a performance of over 401 GFlops on 256 nodes of Appro Xtreme-X3 (648 nodes, 147.2 GFlops/node, 95.4 TFlops peak performance) for 2563-point FFT.
37 citations
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TL;DR: An improved butterfly structure and an address generation method for fast Fourier transform (FFT) using reduced logic to generate the addresses, avoiding the parity check and barrel shifters commonly used in FFT implementations are presented.
Abstract: In this study, an improved butterfly structure and an address generation method for fast Fourier transform (FFT) are presented. The proposed method uses reduced logic to generate the addresses, avoiding the parity check and barrel shifters commonly used in FFT implementations. A general methodology for radix-2 N-point transforms is derived and the signal flow graph for a 16-point FFT is presented. Furthermore, as a case study, a 16-point FFT with 32-bit complex numbers is synthesized using a CMOS 0.18 mum technology. The circuit gate count analysis indicates that significant logic reduction can be achieved with improved throughput compared to the conventional implementations.
36 citations