基于Fourier变换等高线图像插值法

本文基于Ｆｏｕｒｉｅｒ变换提出了场图像的等高线插值法，使场图像恢复为帧图像。通过单方向指定灰度最小波动方法寻找场图像的等高线，将等高线灰度值Ｆｏｕｒｉｅｒ变换后插值，插值后的场图像与实际帧图像比较，并与一些其它插值法比较，结果很理想。     

用初参数法解多层地基的动力问题

本文应用Ｆｏｕｒｉｅｒ积分变换，求出平面多层地基动力问题的初参数解，这些公式简单明了，便于数值计算，不论弹性层数目多少，都不必求解联立方程。     

ODFT的分离基快速算法

ODFT的快速算法是应用多项式变换计算二维循环卷积与二维DFT的关键之一。本文提出了ODFT的分离基快速算法,给出了信号流图,分析了计算复杂性,并和ODFT的其他快速算法作了比较。对实序列的ODFT分离基快速算法,也相应作了探讨。本文算法所需的实乘次数与其它算法相同,而实加次数比其他算法都少。而且可进行原位计算,结构规则,易于实现。     

弹性地基上无限长板受局部荷载作用的解析解

基于Ｋｉｒｃｈｈｏｆｆ薄板驼用Ｆｏｕｒｉｅｒ变换和三角级数法得到了Ｗｉｎｋｌｅｒ地基上无限长板受局部荷载作用的解析解。     

小球在两平行平壁之间的牛顿流体中下落所受的阻力

本文采用奇异摄动方法的匹配法和Ｆｏｕｒｉｅｒ变换方法，求出了小球在两平行平壁之间的牛顿流体中下落所受的阻力，并给出了在小球不同程度偏向一壁情况下的数值计算结果．     

多层半无限弹性体在任意荷载作用下的解析解

本文从柱坐标系下弹性力学基本方程出发，经关于方位角的Ｆｏｕｒｉｅｒ变换及关于径向的Ｈａｎｋｅｌ变换，建立了介质层的传递矩阵，利用层间完全接触条件，给出了多层半无限弹性体在任意荷载作用下的理论解。由于不必要引入应力函数，所以，本方法概念清晰、易懂、便于实际应用。     

双通道无透镜fourier变换计算机全息图

介绍一种制作双通道无透镜Ｆ变换计算机全息图的新方法,用这种方法不仅可以抒情身份个物图象重叠记录在同一张全息图上,而且再现时省去一个Ｆｏｕｒｉｅｒ变换透镜,制作时不需要增加绘图仪的单元数目和尺寸,方法简便。     

利用Fourier变换修正运动图像的失真

本文根据数码相机的摄像原理，通过前后帧图像中物体位置的变化。修正因物体的运动和数码相机扫描时间差造成的图像失真。利用Ｆｏｕｒｉｅｒ变换修正后的结果，对于运动物体特征的提取，具有一定的价值。     

一个能生成一般N Winograd傅里叶交换(WFTA)程序的程序

Winograd傅里叶变换算法(WFTA)是一种新的快速算法,具有乘法次数少、速度快、精确度高等优点,但它的程序设计相当复杂。本文介绍一个能自动生成并打印出任意N点实用程序的程序,大大方便了这种算法的实际应用,已在计量测试研究工作中取得了良好的效果。     

利用哈尔变换分析机械振动冲击信号

本文首先介绍了哈尔变换的数学基础：哈尔函数和哈尔级数及其特点；接着介绍哈尔交换及其逆变换和快速算法（ＦＨＴ＆ＩＦＨＴ）的实现；最后在波谱分析方面与傅里叶变换作了比较，指出了在分析机械振动冲击信号时，哈尔交换更能突出信号特征，更易识别。     

有限元网格图自动生成算法

本文在有限元网格图拓扑分析的基础上,讨论了单元节点拓扑阵自动生成方法和整体节点拓扑阵自动组集方法,并给出了算法。这种方法实现了2D和3D有限元网格图完全自动生成过程,并为单元及节点的相关性分析提供了依据。     

A variable-depth search algorithm for the recursive bipartitioning of signal flow graphs

We discuss the use of local search techniques for mapping video algorithms onto programmable high-performance video signal processors. The mapping problem is very complex due to many constraints that need to be satisfied in order to obtain a feasible solution. The complexity is reduced by decomposing the mapping problem into three subproblems, namely delay management, partitioning, and scheduling. We present the partitioning problem and the representation of video algorithms by signal flow graphs. Furthermore, we propose a solution strategy that is based on recursive bipartitioning of these graphs. The bipartitions are generated using a variable-depth search algorithm. The results demonstrate that the frequently cited flexibility of local search techniques can be successfully exploited in handling complicated problems.     

适合于地震工程信号分析的快速小波变换法研究

本文简要分析了目前普遍采用的小波变换法,指出其尚不能满足地震工程信号分析的要求,由此提出一种直接变换法的改进方法,经详细的考查,证明该方法精度高、速度快,能够满足地震工程信号分析的要求。     

Linear Bijections and the Fast Fourier Transform

 Fast Fourier transform algorithms rely upon the choice of certain bijective mappings between the indices of the data arrays. The two basic mappings used in the literature lead to Cooley–Tukey algorithms or to prime factor algorithms. But many other bijections also lead to FFT algorithms, and a complete classification of these mappings is provided. One particular choice leads to a new FFT algorithm that generalizes the prime factor algorithm. It has the advantage of reducing the floating point operation count by reducing the number of trigonometric function evaluations. A certain equivalence relation is defined on the set of bijections that lead to FFT algorithms, and its connection with isomorphism classes of group extensions is studied. Under this equivalence relation every equivalence class contains bijections leading to an FFT algorithm of the new type. Received October 27, 1994; revised version January 25, 1996     

Remeshing for metal forming simulations—Part I: Two‐dimensional quadrilateral remeshing

In this paper, a general framework of practical two‐dimensional quadrilateral remeshing, which includes the determination of remeshing time, automatic quadrilateral mesh generation, and data transfer process, will be formulated. In particular, the current work contains new algorithms of mesh density specification according to the distribution of effective strain‐rate gradients, mesh density smoothing by fast Fourier transform (FFT) and low‐pass filtering techniques, coarsening it by node placement scheme, and a modified Laplacian mesh smoothing technique. The efficiency of the developed remeshing scheme was tested through three practical two‐dimensional metal forming simulations. The results clearly indicate that the algorithms proposed in this study make it possible to simulate two‐dimensional metal forming problems efficiently and automatically. Copyright © 2002 John Wiley & Sons, Ltd.     

Fast numerical algorithm for the linear canonical transform

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.     

Analysis and Study of Modern Fault Diagnosis Methods of Mechanical Equipments

Fast Fourier Transform（FFT） frequency spectrum analysis, signal decomposing and reconstraction by wavelet analysis, fractal theory and chaos theory are hot research topics for fault diagnosis and prediction of complex machinery so far. In this paper, the characteristics of the FFT method, wavelet method, fractal method, and largest Lyapunov exponent method are studied and analyzed in detail. The advantages and shortcomings of these methods are pointed out respectively. Some unsolved problems are presented here.     

利用射频信号解卷积估计组织和血流运动速度

基于射频信号解卷积,提出了一种无需MTI（Moving Target Indicator）滤波重建血流及组织运动速度的方法。对射频回波的采样序列进行快速傅里叶变换,在频域对相邻两次射频回波的频谱作解卷积处理,通过分析解卷后的数值序列得到组织和血流各自的运动速度。仿真实验对两组典型的时延参数的超声回波信号进行了血流和组织速度的估算,并与给定值比较,证明了方法的有效。该方法有助提高超声血流成像系统对低速血流的测量精度。     

A HEURISTIC METHOD FOR THE AUTOMATIC DRAWING OF SYSTEM MODELING GRAPHS

Graphical modeling formalisms are used for systems analysis and design in several knowledge fields. In the past the graphs associated with a given formalism were produced by hand with the help of templates. Today, however, several computer-aided system modeling tools are available on the market and, in order to be useful, they must be able to quickly display large graphs automatically. Unfortunately, the problem of drawing an arbitrary graph on the plane is NP-hard for most practical drawing criteria. The objective of this paper is to develop heuristic procedures to automatically and timely display arbitrary forests and undirected graphs in an interactive, mouse-driven graphic environment on a micro-computer. A fast geometric algorithm to display a tree with vertices of varying and non-negligible dimensions is presented and a general graph drawing heuristic is derived. The latter is based on the generation of a spanning tree with special properties which can be used to compute the rectangular coordinates of the graph vertices. We conclude with an example and with some comments on the performance of our algorithms.     

Extraction of boundary representation from surface triangulations

Many computational science tools employ finite element meshes as discretizations of the geometrical domains, and automatic mesh generation has become an indispensable part of the discretization process. Boundary representations (BRep) of solids are the means of describing the geometrical model to the mesher, thus enabling the generator to proceed without user intervention. Significant effort has been devoted in the past to BRep construction in the frame‐work of solid modelling systems. In this paper we consider the task of converting a tesselation (triangulation) of the surface of a solid into a BRep, and propose a robust and efficient set of algorithms for this purpose. Applications include, among others, remeshing of finite element discretizations during simulations involving not only geometric distortion but also changes in topology (coalescence and fragmentation of solids, flow, and so on). Copyright © 2001 John Wiley & Sons, Ltd.