平行六边形区域上的快速离散傅立叶变换

In this paper, we propose a fast algorithm for computing the DGFT (Discrete Generalized Fourier Transforms) on hexagon domains [6], based on the geometric properties of the domain. Our fast algorithm (FDGFT) reduces the computation complexity of DGFT from O(N4) to O(N2 log N). In particulary, for N =2^P23^P34^P45^P56^P6, the floating point computation working amount equals to(17/2P2 16p3 135/8p4 2424/25p5 201/2P6)3N^2. Numerical examples are given to access our analysis.     

基于FFT的薄膜厚度干涉测量新方法

在研究二维FFT法进行干涉测试基本原理的基础上,提出一种基于二维FFT的薄膜厚度测量新方法。利用搭建的泰曼-格林型干涉系统,用CCD接收、采集卡采集,可获得被测膜层的干涉条纹图像。编制算法处理软件,可实现对干涉条纹图中薄膜边缘识别、区域延拓、滤波、波面统一等的处理,从而获得带有薄膜信息的面形分布,实现对薄膜样片厚度的自动化测量。研究结果表明：所测薄膜厚度的峰谷值为0．2562,均方根值为0．068λ,说明采用基于FFT的薄膜厚度干涉测量新方法测量薄膜厚度具有较高的精度。     

结构光测量中快速相位解包裹算法的讨论

对Schofield等提出的快速傅里叶变换（采用4次傅里叶变换和4次逆傅里叶）解包裹算法和Volkov等提出的相位重建算法（仅采用两次傅里叶变换和一次逆傅里叶变换）进行了讨论,提出基于离散余弦变换的快速相位解包裹算法.指出前两种算法在处理一般带噪音的模拟相位图时具有明显的优势,其处理结果非常接近理想值,而在处理相位变化剧烈或不连续区域的实验相位图（采用四步相移法测量雕刻佛像的三维面形）时出现较大误差,甚至无法处理,而基于离散余弦变换算法能很好的解决这个问题,并且拥有比前两种算法更快的运算速度.在实际应用中,针对不同的相位图把Schofield所提出的算法与基于离散余弦变换的算法结合起来,可以解决大部分相位解包裹问题.     

THREE-DIMENSIONAL NUMERICAL LOCALIZATION OF IMPERFECTIONS BASED ON A LIMIT MODEL IN ELECTRIC FIELD AND A LIMIT PERTURBATION MODEL

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes： the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.     

脉冲调制射频功率测量中的标定及FFT分析方法研究

利用电压/电流探头和数字示波器实现了脉冲调制射频功率测量。电压/电流探头输出的电压、电流信号由数字示波器采集存储,电压、电流的幅值及相位差由FFT分析得到。在不同频率下,对电压、电流幅值及相位差进行标定,获得计算射频功率的标定参数。分析表明电压、电流相位差是影响标定系数的主要因素,FFT方法处理非稳态调幅电压、电流时存在问题,只有在零无功功率处才能获得可信的吸收功率。     

基于多采样率的复合频率信号频率计设计

研究一种20 Hz～20 kHz双频复合频率的信号频谱在工程技术领域中具有重要应用意义;在对复合频率信号频谱理论分析的基础上,采用了一种多采样率计算复合频率信号频谱的方法,该方法在采用高采样率采集样本进行FFT变换频谱预估计的基础上,利用降采样率的方法再进行一次FFT变换频谱分析,然后结合频谱混叠时信号的频域特征利用预估计的频谱信息计算出高分辨率的频谱信息;该方法计算量适中,可以满足实时性要求;利用TI公司的TMS320F28234 DSP作为处理器构建了一个复合频率信号频率计,可以采集输入的复合频率信号并进行多采样率的频谱分析,经测试该频率计可以实时发送复合频率信号的频谱信息到上位机,频率分辨率达到2 Hz。     

滤波截止频率对粗糙点接触机理影响研究

使用基于快速傅里叶变换和共轭梯度法的接触程序,分析了滤波截止频率对粗糙点接触机理的影响.计算结果表明:粗糙表面形貌数据再处理时使用的滤波器滤波截止频率,对力-接近量关系有着明显的影响;滤波截止频率越小,接触面积越大,接触压力越小;滤波截止频率的改变会导致Von M ises应力的显著改变,这种改变在接触面上特别明显.因此,在实际研究粗糙表面的接触机理时,选择合适的滤波截止频率是非常必要的.     

基于费马素数域高基FFT的RS码快速译码算法

基于数论变换理论,提出了一种新的Rs码频域译码算法,该算法基于以3为成元的费马素数域GF(Fn)高基变换．与常规的以√2生成元的变换相比,该变换提高了最大译码长度;而与以2为基的变换相比,GF(Fn)高基变换．与常规的以√2生成元的变换相比,该变换提高了最大译码长度;而与以2为基的变换相比,c信和卫星通信系统中获得广泛应用的RS(255,223)标准码．     

A direct Schur–Fourier decomposition for the efficient solution of high‐order Poisson equations on loosely coupled parallel computers

In this paper a parallel direct Schur–Fourier decomposition (DSFD) algorithm for the direct solution of arbitrary order discrete Poisson equations on parallel computers is proposed. It is based on a combination of a Direct Schur method and a Fourier decomposition and allows to solve each Poisson equation almost to machine accuracy using only one communication episode. Thus, it is well suited for loosely coupled parallel computers, that have a high network latency compared with the CPU performance. Several three‐dimensional direct numerical simulations (DNS) of wall‐bounded turbulent incompressible flows have been carried out using the DSFD algorithm. Numerical examples illustrating the robustness and scalability of the method on a PC cluster with a conventional 100 Mbits/s network are also presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Detection of edges from spectral data: New results

We are concerned with the problem of recovering edges of piecewise smooth functions with finitely many jump discontinuities. In a series of papers, Gelb and Tadmor presented computationally simple methods for this task that are based on the conjugate Fourier series with different concentration kernels. In this article we present experimental results comparing conjugate series based methods with a new approach based on polynomial filters and suitable approximations. This new approach proves to be more accurate and stable.