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BOUNDARY-CONDITION EXPANSION OF BASIS FUNCTIONS METHOD IMPLEMENTED BY FAST FOURIER-TRANSFORM algorithmS

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1990年第3期38卷 296-301页

作者： STANKOVIC, L JOVICEVIC, S UNIV TITOGRAD DEPT PHYS YU-81000 TITOGRAD YUGOSLAVIA

An approach to boundary value problems is presented. It is based on boundary condition expansion of basis functions. The expansion coefficients are determined using the fast Fourier transform of basis functions on the boundary. This approach is compared with the least-squares boundary residual method (LSBRM). It is shown that this approach results in a considerable reduction in computation time in comparison with the original LSBRM. The procedure is successfully demonstrated on diffraction and eigenvalue problems.

关键词： Basis Coefficient of expansion Boundary computational time basis functions fft algorithm Fast Fourier transform

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A method for selective excitation of Ince-Gaussian modes in an end-pumped solid-state laser

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APPLIED PHYSICS B-LASERS AND OPTICS 2014年第4期117卷 1129-1134页

作者： Lei, J. Hu, A. Wang, Y. Chen, P. Huazhong Univ Sci & Technol Sch Opt & Elect Informat Wuhan 430074 Peoples R China

A method for selective excitation of Ince-Gaussian modes is presented. The method is based on the spatial distributions of Ince-Gaussian modes as well as the transverse mode selection theory. Significant diffraction loss is introduced in a resonator by using opaque lines at zero-intensity positions, and this loss allows to excite a specific mode;we call this method "loss control.'' We study the method by means of numerical simulation of a half-symmetric laser resonator. The simulated field is represented by angular spectrum of the plane waves representation, and its changes are calculated by the two-dimensional fast Fourier transform algorithm when it passes through the optical elements and propagates back and forth in the resonator. The output lasing modes of our method have an overlap of over 90 % with the target Ince-Gaussian modes. The method will be beneficial to the further study of properties and potential applications of Ince-Gaussian modes.

关键词： diffraction loss DIODE-PUMPED SOLID STATE LASERS Excitation fft algorithm solid state lasers Resonator Device Component Optical Component

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Optimized circularly symmetric phase mask to extend the depth of focus

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2009年第8期26卷 1889-1895页

作者： Zhou, Feng Ye, Ran Li, Guangwei Zhang, Haitao Wang, Dongsheng Tsinghua Univ Dept Precis Instrument & Mechanol Beijing 100084 Peoples R China Xidian Univ Sch Tech Phys Xian 710071 Peoples R China Equipment Acad AF Inst Radar & Elect Countermeasure Beijing 100085 Peoples R China

We propose a novel design method for a circularly symmetric phase mask to extend the depth of focus. Using the free-form rational function as the solution space, we optimize the profile of the phase mask by analysis of the axial intensity distribution, which can be calculated efficiently by employing the fast Fourier transform algorithm. Numerical comparisons prove the resulting rational phase mask's superiority to the existing quartic phase mask in intensity distribution and imaging performance. (C) 2009 Optical Society of America

关键词： Phase Mask design approach symmetric phase intensity distribution Solution space rational functions fft algorithm DEPTH OF FIELD

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On the efficient computation of single-bit input word length pipelined ffts

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IEICE ELECTRONICS EXPRESS 2011年第17期8卷 1437-1443页

作者： Athar, Saima Gustafsson, Oscar Qureshi, Fahad Kale, Izzet Linkoping Univ Dept Elect Engn SE-58183 Linkoping Sweden Univ Westminster Appl DSP & VLSI Res Grp London W1W 6UW England

This letter describes an efficient architecture for the computation of fast Fourier transform (fft) algorithms with single-bit input. The proposed architecture is aimed for the first stages of pipelined fft architectures, processing one sample per clock cycle, hence making it suiable for real-time fft computation. Since natural input order pipeline ffts use large memories in the early stages, it is important to keep the word length shorter in the beginning of the pipeline. By replacing the initial butterflies and rotators of an architecture with that of the proposed block, the memory requirements can be significantly reduced. Comparisons with the commonly used single delay feedback (SDF) architecture show that more than 50% of the required memory can be saved in some cases.

关键词： fft algorithm complexity single-bit word length

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Modeling of widely tunable V-cavity semiconductor laser using time-domain traveling-wave method

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 2015年第2期32卷 309-317页

作者： Wu, Lin He, Jian-Jun Gallagher, Dominic Zhejiang Univ State Key Lab Modern Opt Instrumentat Dept Opt Engn Hangzhou 310027 Zhejiang Peoples R China Photon Design Ltd Oxford OX4 1TW England

We investigate the static and dynamic characteristics of the widely tunable V-cavity semiconductor laser using the time-domain traveling-wave method. The theoretical model is presented. The simulation results are compared with experimental data for an all-active V-cavity laser, and good agreements are obtained. To improve the device performance, a new device structure with passive tuning waveguides is designed. The numerical results show that 21 channels can be achieved by single electrode tuning using carrier injection effect with two cavities of 420 and 440 mu m long. Dynamic wavelength switching between different channels is simulated. Mode competition is observed during the transient and the switching delay time varies from 3 to 18.5 ns for different switching paths. A simple algorithm for quasi-continuous tuning is developed for the first time by varying the injection currents on the channel selector electrode and the fine-tuning electrode synchronously. A quasi-continuous tuning of 16.8 nm is achieved with a current variation of less than 20 mA on each electrode. For direct modulation characteristics, small signal response simulation is carried out by an impulse current injection with a fast Fourier transform algorithm, and a 3 dB bandwidth of 7 GHz is obtained when biased at 100 mA. Moreover, 2.5 and 10 Gb/s direct intensity modulation are also demonstrated. The simulation results show great potential for the compact and low-cost tunable laser to be used for wavelength-agile access and data center networks, as well as biomedical applications. (C) 2015 Optical Society of America

关键词： Semiconductor lasers Simulation results carrier injection tuning intensity modulation Electrodes Double cavity Tunable lasers equipment performance fft algorithm Modeling

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Estimating the Parameters of Sinusoids and Decaying Sinusoids in Noise

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IEEE INSTRUMENTATION & MEASUREMENT MAGAZINE 2011年第2期14卷 8-14页

作者： Aboutanios, Elias Univ Edinburgh Inst Digital Commun Edinburgh EH8 9YL Midlothian Scotland

Picture a low earth orbit satellite hurtling around the earth in an 800 km orbit. At this altitude, the satellite travels about 7.5 km every second, and any signals between it and an earth terminal experience significant Doppler shifts. These frequency offsets must be estimated and removed at the earth terminal to enable successful communications with the satellite. As in this example, the estimation of the parameters of a sinusoid plays a fundamental role in a variety of applications ranging from seismology to radar and biological signals. Therefore, this problem has received, and continues to receive, significant attention in the literature. In power delivery systems, the estimation of the supply frequency is required for the monitoring of the system quality and the detection of faults [1], [2]. In nuclear magnetic resonance spectroscopy (NMRS), on the other hand, the signal is modelled as a sum of decaying complex exponentials whose frequencies and decay factors must be estimated [3]. The advent of computing and the subsequent introduction of the fast Fourier transform (fft) algorithm revolutionized the digital processing of signals. The fft algorithm provides a highly efficient implementation of the discrete Fourier transform (DFT) on a regularly sampled grid. This efficiency and suitability for fast implementations on digital signal processors have made the fft a very successful and widely used algorithm. It is no surprise that it has come to form the basis for a significant number of parameter estimators.

关键词： Parameter estimation fft algorithm close-orbit satellite Earth terminals power delivery systems Fast Fourier transform Digital signal processors signals satellites

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Dimension-reduction simulation of stochastic wind velocity fields by two continuous approaches

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WIND AND STRUCTURES 2019年第6期29卷 389-403页

作者： Liu, Zhangjun He, Chenggao Liu, Zenghui Lu, Hailin Wuhan Inst Technol Sch Civil Engn & Architecture Wuhan 430074 Hubei Peoples R China China Three Gorges Univ Coll Civil Engn & Architecture Yichang 443002 Peoples R China

In this study, two original spectral representations of stationary stochastic fields, say the continuous proper orthogonal decomposition (CPOD) and the frequency-wavenumber spectral representation (FWSR), are derived from the Fourier-Stietljes integral at first Meanwhile, the relations between the above two representations are discussed detailedly. However, the most widely used conventional Monte Carlo schemes associated with the two representations still leave two difficulties unsolved, say the high dimension of random variables and the incompleteness of probability with respect to the generated sample functions of the stochastic fields. In view of this, a dimension-reduction model involving merely one elementary random variable with the representative points set owing assigned probabilities is proposed, realizing the refined description of probability characteristics for the stochastic fields by generating just several hundred representative samples with assigned probabilities. In addition, for the purpose of overcoming the defects of simulation efficiency and accuracy in the FWSR, an improved scheme of non-uniform wavenumber intervals is suggested. Finally, the Fast Fourier Transform (fft) algorithm is adopted to further enhance the simulation efficiency of the horizontal stochastic wind velocity fields. Numerical examples fully reveal the validity and superiority of the proposed methods.

关键词： stochastic wind velocity field continuous proper orthogonal decomposition frequency-wavenumber spectral representation dimension reduction non-uniform wavenumber intervals fft algorithm

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Frequency-domain weighted non-linear least-squares estimation of continuous-time, time-varying systems

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IET CONTROL THEORY AND APPLICATIONS 2011年第7期5卷 923-933页

作者： Lataire, J. Pintelon, R. Vrije Univ Brussel Dept ELEC Fundamental Elect & Instrumentat B-1050 Brussels Belgium

A frequency-domain least-squares estimator is presented for identifying linear, continuous-time, time-varying dynamical systems. The model considered is a linear, ordinary differential equation whose coefficients vary as polynomials in time. A frequency-domain approach is used, thus allowing the user to determine easily the frequency band(s) of interest. It is shown that the bias errors because of windowing and sampling the continuous-time signals can be modelled by a polynomial function of the frequency. The regression matrices of the estimators are shown to be very efficiently computed using the fast Fourier transform algorithm and its inverse. The total least-squares, generalised total least-squares and weighted, non-linear least-squares estimators are constructed. The latter two are shown to be consistent. The estimators are illustrated on simulation and measurement data.

关键词： Frequency function Estimators time-varying systems fft algorithm Frequency bands Ordinary differential equation measurement data Polynomial multiprogramming least-squares estimator

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SCATTERING FROM ROUGH SURFACES - A NEW APPROXIMATE THEORY

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JOURNAL OF OPTICS-NOUVELLE REVUE D OPTIQUE 1988年第2期19卷 51-57页

作者： FAUREGEORS, H MAYSTRE, D ROGER, A Lab. d'Opt. Electromagn. CNRS Fac. des Sci. et Tech. Marseille France

A new approximate method for problems of scattering from rough surfaces is introduced. Its numerical implementation is achieved by using a Fast Fourier Transform algorithm and leads to small computation times. The results for diffraction gratings and non periodic rough surfaces are checked by comparison with rigorous results. It is shown that the precision of the new method is much better than that provided by the Kirchhoff approximation.

关键词： Rough surfaces Diffraction gratings Scattering Approximate Kirchhoff&apos s Law Precision fft algorithm broadcasting Understory

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Multidimensional fast Fourier transform algorithm for signals with arbitrary symmetries

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 1999年第8期16卷 1892-1908页

作者： Bernardini, R Cortelazzo, G Mian, GA Univ Padua Dipartimento Elettron & Informat I-35131 Padua Italy

A multidimensional fast Fourier transform (fft) algorithm is presented for signals with arbitrary symmetries and periodic on arbitrary lattices. Applications that can benefit from such an algorithm include Volterra filtering and analysis of x-ray diffraction data. The presented algorithm exploits signal redundancy to achieve a computational complexity of N log N, where N is the number of independent samples. To the authors' knowledge, this is the only fft that;makes the frequency domain computation of Volterra filtering more convenient than the time domain approach. (C) 1999 Optical Society of America [S0740-3232(99)02108-0].

关键词： Nonlinear filters TIME-DOMAIN algorithms MULTIDIMENSIONAL complexity classes signals Arbitrary fft algorithm X-ray diffraction data Fast Fourier transform

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