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fast Numerical Nonlinear Fourier Transforms

IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第12期61卷 6957-6974页

作者： Wahls, Sander Poor, H. Vincent Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schrodinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them-at least from a theoretical point of view. Although numerical algorithms are available for computing the transform, a fast nonlinear Fourier transform that is similarly effective as the fast Fourier transform is for computing the common Fourier transform has not been available so far. The goal of this paper is to address this problem. Two fast numerical methods for computing the nonlinear Fourier transform with respect to the NSE are presented. The first method achieves a runtime of O(D-2) floating point operations, where D is the number of sample points. The second method applies only to the case where the NSE is defocusing, but it achieves an O(D log(2) D) runtime. Extensions of the results to other evolution equations are discussed as well.

关键词： Nonlinear Fourier transform forward scattering transform nonlinear Schrodinger equation fast algorithms

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fast algorithm for discrete fractional Hadamard transform

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NUMERICAL algorithms 2015年第3期68卷 585-600页

作者： Cariow, Aleksandr Majorkowska-Mech, Dorota West Pomeranian Univ Technol Fac Comp Sci & Informat Technol Szczecin Poland

This paper proposes a fast algorithm for computing the discrete fractional Hadamard transform for the input vector of length N, being a power of two. A direct calculation of the discrete fractional Hadamard transform requires N (2) real multiplications, while in our algorithm the number of real multiplications is reduced to N log (2) N.

关键词： Discrete linear transforms Discrete fractional Hadamard transform Eigenvalue decomposition fast algorithms

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fastME 2.0: A Comprehensive, Accurate, and fast Distance-Based Phylogeny Inference Program

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MOLECULAR BIOLOGY AND EVOLUTION 2015年第10期32卷 2798-2800页

作者： Lefort, Vincent Desper, Richard Gascuel, Olivier CNRS UMR 5506 LIRMM Inst Biol Computat F-75700 Paris France Univ Montpellier Montpellier France

fastME provides distance algorithms to infer phylogenies. fastME is based on balanced minimum evolution, which is the very principle of Neighbor Joining (NJ). fastME improves over NJ by performing topological moves using fast, sophisticated algorithms. The first version of fastME only included Nearest Neighbor Interchange. The new 2.0 version also includes Subtree Pruning and Regrafting, while remaining as fast as NJ and providing a number of facilities: Distance estimation for DNA and proteins with various models and options, bootstrapping, and parallel computations. fastME is available using several interfaces: Command-line (to be integrated in pipelines), PHYLIP-like, and a Web server (http://***/fastme/).

关键词： phylogeny inference distance-based fast algorithms (balanced) minimum evolution NNI and SPR topological moves

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fast Inverse Nonlinear Fourier Transform for Generating Multi-Solitons in Optical Fiber

Fast Inverse Nonlinear Fourier Transform for Generating Mult...

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IEEE International Symposium on Information Theory (ISIT)

作者： Wahls, Sander Poor, H. Vincent Delft Univ Technol Delft Ctr Syst & Control Delft Netherlands Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

ISBN: (纸本)9781467377041

The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only O(D log(2)D) floating point operations to compute D samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with log(2)-linear complexity. The paper also includes a many-samples analysis of the generated nonlinear Fourier spectra.

关键词： Nonlinear Fourier Transform fast algorithms Optical Fiber Nonlinear Schrodinger Equation Solitons

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Generalized convolution quadrature with variable time stepping. Part II: Algorithm and numerical results

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APPLIED NUMERICAL MATHEMATICS 2015年 94卷 88-105页

作者： Lopez-Fernandez, Maria Sauter, Stefan GSSI I-67100 Laquila Italy Univ Zurich Inst Math CH-8057 Zurich Switzerland

In this paper we address the implementation of the Generalized Convolution Quadrature (gCQ) presented and analyzed by the authors in a previous paper for solving linear parabolic and hyperbolic convolution equations. Our main goal is to overcome the current restriction to uniform time steps of Lubich's Convolution Quadrature (CQ). A major challenge for the efficient realization of the new method is the evaluation of high-order divided differences for the transfer function in a fast and stable way. Our algorithm is based on contour integral representation of the numerical solution and quadrature in the complex plane. As the main application we consider the wave equation in exterior domains, which is formulated as a retarded boundary integral equation. We provide numerical experiments to illustrate the theoretical results. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Variable step size Convolution quadrature Convolution equations Retarded potentials Boundary integral equations Wave equation fast algorithms Contour integral methods

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GPU Accelerated Multilevel fast Physical Optics Algorithm for Radiation from Non-Planar Apertures

GPU Accelerated Multilevel Fast Physical Optics Algorithm fo...

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IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS)

作者： Milo, Matan Galanti, Barak Boag, Amir Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

ISBN: (纸本)9781479974733

Acceleration of the multilevel physical optics (MLPO) algorithm using the single instruction multiple threads (SIMT) computing scheme, as implemented on a CUDA-architecture based GPU accelerator is presented. The MLPO algorithm already reduces the computing complexity (CC) of the physical optics based radiation pattern calculation algorithm to O(N(2)logN), as compared to the O(N-3) or O(N-4) CC of the straight-forward implementation (depending on the nature of the problem). Here, N=kR, R being the radius of the smallest sphere containing the radiating aperture and k - the wavenumber. By implementing on a CPU, the MLPO algorithm is accelerated tenfold, allowing fast and efficient evaluation of physical optics integrals. Performance improving optimizations of the parallel code are described. Finally, a timing model that provides estimates of the GPU computation time is presented and compared to the actual GPU run-time measurements.

关键词： Antennas fast algorithms graphic processing units (CPU) physical optics

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VLSI Computational Architectures for the Arithmetic Cosine Transform

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IEEE TRANSACTIONS ON COMPUTERS 2015年第9期64卷 2708-2715页

作者： Rajapaksha, Nilanka Madanayake, Arjuna Cintra, Renato J. Adikari, Jithra Dimitrov, Vassil S. Univ Akron Dept Elect & Comp Engn Akron OH 44325 USA Univ Calgary Dept Elect & Comp Engn Calgary AB Canada Univ Akron Dept Elect & Comp Engn Akron OH 44325 USA Univ Fed Pernambuco Dept Estat Signal Proc Grp Recife PE Brazil Ellipt Technol Inc Ottawa ON Canada

The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier intensive, and accumulate round-off errors. Recently proposed fast algorithm arithmetic cosine transform (ACT) calculates the DCT exactly using only additions and integer constant multiplications, with very low area complexity, for null mean input sequences. The ACT can also be computed non-exactly for any input sequence, with low area complexity and low power consumption, utilizing the novel architecture described. However, as a trade-off, the ACT algorithm requires 10 non-uniformly sampled data points to calculate the eight-point DCT. This requirement can easily be satisfied for applications dealing with spatial signals such as image sensors and biomedical sensor arrays, by placing sensor elements in a non-uniform grid. In this work, a hardware architecture for the computation of the null mean ACT is proposed, followed by a novel architectures that extend the ACT for non-null mean signals. All circuits are physically implemented and tested using the Xilinx XC6VLX240T FPGA device and synthesized for 45 nm TSMC standard-cell library for performance assessment.

关键词： Discrete cosine transform arithmetic cosine transform fast algorithms VLSI

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fast Algorithm for Precise Estimation of Fundamental Frequency on Short Time Intervals 17th

Fast Algorithm for Precise Estimation of Fundamental Frequen...

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17th International Conference on Speech and Computer (SPECOM)

作者： Barabanov, Andrey Melnikov, Alexandr Magerkin, Valentin Vikulov, Evgenij St Petersburg State Univ St Petersburg 199034 Russia

ISBN: (纸本)9783319231327;9783319231310

fast algorithms are proposed for precise estimation of the Fundamental frequency on a short time interval. The approach is a generalization of the unbiased frequency estimator. Its computational complexity is proportional to that of FFT on the same time interval. A trade-off between approximation error and numerical speed is established. The result is generalized to the linear trend model. The lower bound is obtained for the time interval length with a nonsingular information matrix in the estimation problem. The frequency estimation algorithm is not sensitive to big random noises.

关键词： Frequency estimation fast algorithms Harmonic model

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A TRIVARIATE INTERPOLATION ALGORITHM USING A CUBE-PARTITION SEARCHING PROCEDURE

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2015年第4期37卷 A1891-A1908页

作者： Cavoretto, Roberto De Rossi, Alessandra Univ Turin Dept Math G Peano I-10123 Turin Italy

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm.

关键词： meshless approximation fast algorithms partition of unity methods radial basis functions scattered data

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Multilevel Physical Optics Algorithm for Near-Field Double-Bounce Scattering

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2015年第11期63卷 5015-5025页

作者： Roudstein, Moty Brick, Yaniv Boag, Amir Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA

A fast algorithm for the evaluation of the double-bounce (DB) contributions to the physical optics scattering integrals, over a range of aspect angles and frequencies, is presented. The work extends the preceding far-field algorithm, to encompass three-dimensional and near-field scenarios. The algorithm relies on multilevel sampling and interpolation of phase- and amplitude-compensated contributions of subdomain pairs. A particular design of the phase- and amplitude-compensation functions and sampling grids, tailored to the DB near-field case, is presented. The improved performance and error controllability are demonstrated via representative examples.

关键词： fast algorithms high-frequency methods physical optics (PO) scattering cross section

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