On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equations

In this paper, we consider a piecewise linear collocation method for the solution of a pseudo‐differential equation of order r=0, ?1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the wavelet basis in the trial space we choose the three‐point hierarchical basis together with a slight modification near the boundary points of the global patches of parametrization. We choose linear combinations of Dirac delta functionals as wavelet basis in the space of test functionals. For the corresponding wavelet algorithm, we show that the parametrization can be approximated by low‐order piecewise polynomial interpolation and that the integrals in the stiffness matrix can be computed by quadrature, where the quadrature rules are composite rules of simple low‐order quadratures. The whole algorithm for the assembling of the matrix requires no more than O(N [logN]³) arithmetic operations, and the error of the collocation approximation, including the compression, the approximative parametrization, and the quadratures, is less than O(N^?(2?r)/2). Note that, in contrast to well‐known algorithms by Petersdorff, Schwab, and Schneider, only a finite degree of smoothness is required. In contrast to an algorithm of Ehrich and Rathsfeld, no multiplicative splitting of the kernel function is required. Beside the usual mapping properties of the integral operator in low order Sobolev spaces, estimates of Calderón–Zygmund type are the only assumptions on the kernel function. Copyright © 2003 John Wiley & Sons, Ltd.     

Quadrature Formulas for Refinable Functions and Wavelets II: Error Analysis

This paper is concerned with the construction and the analysis of Gauss quadrature formulas for computing integrals of (smooth) functions against refinable functions and wavelets. The main goal of this paper is to develop rigorous error estimates for these formulas. For the univariate setting, we derive asymptotic error bounds for a huge class of weight functions including spline functions. We also discuss multivariate quadrature rules and present error estimates for specific nonseparable refinable functions, i.e., for some special box splines.     

Higher-order quadratures for circulant preconditioned Wiener-Hopf equations

In this paper, we consider solving matrix systems arising from the discretization of Wiener-Hopf equations by preconditioned conjugate gradient (PCG) methods. Circulant integral operators as preconditioners have been proposed and studied. However, the discretization of these preconditioned equations by employing higher-order quadratures leads to matrix systems that cannot be solved efficiently by using fast Fourier transforms (FFTs). The aim of this paper is to propose new preconditioners for Wiener-Hopf equations. The discretization of these preconditioned operator equations by higher-order quadratures leads to matrix systems that involve only Toeplitz, circulant and diagonal matrix-vector multiplications and hence can be computed efficiently by FFTs in each iteration. We show that with the proper choice of kernel functions of Wiener-Hopf equations, the resulting preconditioned operators will have clustered spectra and therefore the PCG method converges very fast. Numerical examples are given to illustrate the fast convergence of the method and the improvement of the accuracy of the computed solutions with using higher-order quadratures.Research supported by the Cooperative Research Centre for Advanced Computational Systems.Research supported in part by Lee Ka Shing scholarship.     

正交检波器通道间平衡性能测试的线性回归方法

提出了一种测量正交检波器通道间幅度不平衡性和相位不平衡性的新方法——线性回归方法，并用计算机进行了数值模拟。模拟结果表明，该方法的计算精度很高。     

模拟正交调制器性能优化设计

主要介绍了模拟正交调制器性能优化设计方法，推导出调制器性能与相关参数之间的关系，实现其性能优化设计的方法，并给出了调制器性能与相关参数的关系图。     

基于DDC的镜像干扰抑制

在通信信号和雷达信号处理中，通常需要将信号正交分解为两路正交的I，Q信号。然后再做进一步的处理，而I，Q通道间抚养益误差和相位误差会造成镜像干扰。影响系统性能，文中分析了I，Q通道的增益误差和正交误差对镜像干扰抑制比的影响，用实验验证了采用HSP50016后对镜像干扰抑制的改善。     

Differential quadrature domain decomposition method for problems on a triangular domain

The differential quadrature method (DQM) has been studied for years and it has been shown by many researchers that the DQM is an attractive numerical method with high efficiency and accuracy. The conventional DQM is mostly effective for one‐dimensional and multidimensional problems with geometrically regular domains. But to deal with problems on a triangular domain, we will meet difficulties. In this article we will study how to solve problems on a triangular domain by using DQM combined with the domain decomposition method (DDM). © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Multivalued Analytic Continuation of the Cauchy Transform

In this paper we introduce the notion of multivalued analytic continuation of the Cauchy transforms. Many difficulties arise because the continuation is not single-valued. Our main result asserts that if χ_Ω has a multivalued analytic continuation, then the free boundary ∂Ω has zero Lebesgue measure. Here χ_Ω is the characteristic function of a domain Ω and ∂Ω is its boundary. We also discuss the connections between this notion, quadrature domains and approximations of analytic functions with single-valued integrals by rational functions. The last problem is related to the existence of a continuous function g and a closed connected set K such that the gradient of g vanishes on K, nevertheless g is not constant on K. Mathematics Subject Classifications (2000) Primary 31A25, 31B20; secondary 30E10, 35J05, 41A20.     

军用电子产品筛选方法的优化

主要介绍了如何利用正态分布和正态优化对现有的筛选方法进行优化，从而使优化后的筛选方法在达到预期筛选目的的情况下做到最经济，省时和有效。     

DAB接收机中改进的数字下变频算法及实现

为了有效地降低直接中频采样所带来的硬件开销,到目前为止,已经有很多种复杂的采样技术被提出.其中,4倍中频采样算法得到了广泛的应用.本文在此基础上提出了一种相位补偿方案以解决I、Q通道的失配.同时,对这种改进的基于4倍中频采样的数字下变频算法进行了仿真,并成功地将之应用于DAB接收机的芯片设计.