柯林斯公式的D-FFT计算

将柯林斯公式及其逆运算表示为卷积形式,导出对应的传递函数,讨论使用快速傅里叶变换(FFT)计算柯林斯公式时满足取样定理的条件,基于研究结果,给出光波通过一光学系统的衍射场计算及根据衍射场重建入射平面光波场的实例。     

风场模拟中AR模型的若干问题

自回归(AR)模型具有计算量小,模拟速度快等优良特性,在风场模拟中得到了广泛应用.本文对AR模型进行了系统的研究,将脉动风场模拟中广泛应用的AR模型归为两大类,对模型中的参数从理论上进行了合理的解释.对两种模型模拟脉动风场时涉及到的Wiener-KJaintchine公武的交换形式,通过分析对其进行了修正,指出算法上可以采用FFT技术来计算互相关矩阵的元素以提高计算效率.提出了AR模型编程中偶然发现的自回归顺序问题,算例表明两种不同方法的风速时程样本及其无偏自相关估计和自功率谱估计均有较大的影响,希望能引起更多同行对该问题的注意.尽管标量过程AR模型简单且易于掌握,但不能考虑时滞问题.相比之下,理论分析和数值实验都证明,向量过程的AR模型在精度总体要高于标量过程的AR模型,但其运算时间也相应增多.     

激光辐照下非稳腔镜变形对激光模式的影响

 分析了正支虚共焦非稳腔中腔镜变形对激光模式的影响,采用时间离散化、快速傅里叶变换（FFT）和有限元分析(FEA)方法解决腔镜变形和激光模式两者之间的耦合问题。计算结果表明,随着激光器工作时间的增加,腔镜温升和变形相应增大,谐振腔模式变差,输出光场相位均匀性变差,呈现散焦现象,输出光束质量下降。实验验证了激光器输出光束质量随出光时间的延长而逐渐变坏。     

面向空气信道传播的音频信息隐写算法

基于傅立叶变换,提出了一种面向空气信道传播音频信息隐写算法.该算法选取原始音频信号傅立叶变换域中的低频系数,提取其相位角系数,并对其进行修改,将经BCH纠错编码的隐写信息嵌入,并且嵌入量较大,隐藏效果好.实验结果显示,该算法能够有效抵抗空气传播过程中的AD/DA变换攻击、空气噪声干扰攻击,以及录制后的常见信号处理攻击、约30%的重采样攻击等其他攻击,平均误码率可控制在3.5%以下,算法具有很好的鲁棒性.     

Numerical Simulation of Antennas with Improved Integral Equation Method

Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object.     

关于(R,r)-循环分块矩阵求逆与相乘的一种快速算法

利用矩阵分块逐次降阶的方法和快速富里叶变换(FFT),给出了mn阶(R,r)-循环分块矩阵求逆与相乘的一种快速算法,证明了其计算复杂性为O(mnlog2mn).     

COMPACT FOURTH-ORDER FINITE DIFFERENCE SCHEMES FOR HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS

In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the O（h^4） term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.     

A FAST COMPACT DIFFERENCE METHOD FOR TWO-DIMENSIONAL NONLINEAR SPACE-FRACTIONAL COMPLEX GINZBURG-LANDAU EQUATIONS

This paper focuses on a fast and high-order finite difference method for two-dimensional space-fractional complex Ginzburg-Landau equations.We firstly establish a three-level finite difference scheme for the time variable followed by the linearized technique of the nonlinear term.Then the fourth-order compact finite difference method is employed to discretize the spatial variables.Hence the accuracy of the discretization is O(τ2 + h41 +h42) in L2-norm,where τ is the temporal step-size,both h1 and h2 denote spatial mesh sizes in x-and y-directions,respectively.The rigorous theoretical analysis,including the uniqueness,the almost unconditional stability,and the convergence,is studied via the energy argument.Practically,the discretized system holds the block Toeplitz structure.Therefore,the coefficient Toeplitz-like matrix only requires O(M1M2) memory storage,and the matrix-vector multiplication can be carried out in O(M1M2(logM1 + log M2))computational complexity by the fast Fourier transformation,where M1 and M2 denote the numbers of the spatial grids in two different directions.In order to solve the resulting Toeplitz-like system quickly,an efficient preconditioner with the Krylov subspace method is proposed to speed up the iteration rate.Numerical results are given to demonstrate the well performance of the proposed method.     

润滑接触中弹性变形的快速数值计算

研究了弹性变形的计算特点 ,并在简单回顾卷积算法的基础上给出了一种利用快速傅立叶变换 (FFT)和离散圆卷积计算弹性变形的方法 .计算表明 ,通过对压力信号和影响系数 -响应函数 (Green函数 )进行简单的预处理 ,可以获得准确的弹性变形 ,其计算精度和多层网格积分法相当 ,而计算速度则是多层网格积分法的 3倍左右 ,是一种准确、高效的数值计算方法     

基于位相相关检测的图像配准算法

分析了传统的傅里叶-梅林变换和最近提出的虚拟极坐标傅里叶变换算法在户外图像注册中的局限性,提出了一种更加适合户外摄像机姿态注册的基于对数傅里叶变换的图像配准算法。该算法能够独立地计算沿两坐标轴方向的不同缩放因子和计算两图像间较大的旋转角度,扩展了基于傅里叶变换的图片配准算法的实际应用范围。在关键技术研究方面,提出了由升余弦函数构成的低通滤波器和一种快速收敛的角度搜索技术,使该算法达到了很高的效率和鲁棒性。