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 simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization that operates over the gradient of the phase jumps by a robust and noniterative scheme that could be used in metrological interferometric and fringe-projection automatic real-time applications.
Abstract: A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm’s performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.
29 citations
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TL;DR: The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion and is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method.
Abstract: This paper describes a fast direct algorithm for obtaining least-squares phase estimates from arrays of noisy phase differences. The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion. It is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method. The effectiveness of the algorithm has been demonstrated by using it in connection with the Knox–Thompson speckle-imaging procedure to restore an optical object perturbed by simulated atmospheric turbulence. Representative results are discussed in the paper.
29 citations
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TL;DR: Experimental results show that the proposed feedforward FFT hardware architectures reduce the hardware cost significantly with respect to previous FFT architectures.
Abstract: In this paper, we present new feedforward FFT hardware architectures based on rotator allocation. The rotator allocation approach consists in distributing the rotations of the FFT in such a way that the number of edges in the FFT that need rotators and the complexity of the rotators are reduced. Radix-2 and radix-2 k feedforward architectures based on rotator allocation are presented in this paper. Experimental results show that the proposed architectures reduce the hardware cost significantly with respect to previous FFT architectures.
29 citations
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TL;DR: In this article, a hybrid algorithm based on the GA and modified iterative Fourier transform (MIFT) technique called HGAMIFT is proposed for large thinned array synthesis, which can achieve a better solution in terms of the peak sidelobe level when compared to the iterative FFT technique.
Abstract: In this letter, a hybrid algorithm based on the genetic algorithm (GA) and modified iterative Fourier transform (MIFT) technique called HGAMIFT is proposed for large thinned array synthesis. By employing a perturbation mechanism, the MIFT can achieve a better solution in terms of the peak sidelobe level when compared to the iterative Fourier transform technique. Moreover, a control factor to determine the proportion of individuals from GA and MIFT as well as the crossover and mutation rate is introduced to help the HGAMIFT maintain the diversity of population in the early phase while avoiding stagnation in the late phase. Thus, a resulting enhanced search ability and fast convergence velocity can be obtained simultaneously. Several thinned arrays that comprise different array sizes and aperture shapes have been synthesized, which validate the superior performance of the proposed algorithm.
29 citations
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TL;DR: In this article, the maximal rank-deficient submatrices of Fourier matrices with order a power of a prime number were considered, and a hierarchical subdivision of these matrices into low rank blocks was considered.
28 citations