Matrix Approximation Techniques for Symbolic Extraction of Poles and Zeros

Several recently published approaches to symbolic pole/zero analysis of analog circuits exploit the order reduction effect of Simplification Before Generation (SBG) techniques [1]. SBG methods allow the extraction of symbolic expressions for poles and zeros by computing local low-order approximations of transfer functions whose roots can be calculated analytically. In this article we present a new matrix-based SBG method for pole/zero analysis which simplifies a symbolic generalized eigenvalue problem with respect to a selected root. The method uses a fast linear error estimation formula based on eigenvalue sensitivities to obtain a term ranking. Accurate and efficient error control is achieved by tracking eigenvalue shifts numerically using an iterative generalized eigenvalue solver. The new algorithm is capable of computing real and complex dominant as well as unobservable poles and zeros.     

The generalized eigenproblem: pole-zero computation

A modification-decomposition (MD) method is used to compute linear system transfer function poles and zeros by transforming an N-dimensional generalized eigenvalue problem to an M-dimensional standard eigenvalue problem with M⩾ r, where r is the lesser of the ranks of the dynamic or nondynamic component matrix of the system. Hence, network eigenvalue problems normally solved by applying the QZ algorithm directly, or after deflation preprocessing, are solvable with the more efficient QR algorithm. It is shown that the flop (floating-point operations) count for MD-QR algorithms is always less than the flop count for the most efficient deflation-QZ algorithms. For r⩽N, the MD-QR algorithms are exceptionally efficient. Using a parameter matrix decomposition of the dynamic or nondynamic component matrix, the MD method gives physical insight, and it provides a general proof of manifold constraints relating network time constants and poles and zeros. From these relations, accurate dominant and subdominant pole approximations are derived. A general eigenvalue sensitivity formula and a very flexible method for computing eigenvectors is developed and applied to pole sensitivity computation     

再论X（K）有零点的卷积反演的DFT算法

本文提出X[k]有零点而Y[k]无这些零点的卷积反演的DFT方法。     

On the Complete Eigenvalue Solution of Ridged Waveguide

The complete solution of the ridged waveguide eigen-value problem is presented. The solution is obtained by the formulation of an integral eigenvalue equation which is subsequently solved numerically by application of the Ritz-Galerkin method. The significance of the eigenvalue spectrum is discussed and the modes are classified as either hybrid or trough modes. Equations are given for the electric and magnetic fields and a brief discussion of the edge singularity is presented. The theory is illustrated by computing the dominant eigenvalues and characteristic impedances of various unsymmetrical ridged waveguides.     

低信噪比双基地MIMO雷达目标角度跟踪算法

研究了低信噪比时双基地MIMO雷达目标跟踪问题,提出了一种基于改进AAJD（Adaptive Asymmetric Joint Diagonalization）的目标跟踪算法.首先,对AAJD算法进行改进,得到与特征值作用相同的变量,从而找出大特征值变量对应的特征矢量,解决了低信噪比时AAJD算法信号子空间扩展问题.其次,在非稳定跟踪状态时消除特征值变量误差积累的影响,得到更加准确的信号子空间,并对ESPRIT算法进行改进,实现收发角度的配对和相邻时刻角度的自动关联.仿真结果表明改进AAJD算法低信噪比时能够实现角度跟踪,且收敛速度和稳定性能明显优于AAJD算法.     

一种基于三正交约束的摄像机标定方法

提出一种基于三正交约束的摄像机标定方法.设定摄像机坐标系为世界坐标系,标定摄像机内参数中的5个未知量和1个投影缩放因子,设计一种由7个空间点组成的标定模板,在不需要已知标定模板线段长度的情况下,仅需要2幅以上不同姿态标定模板的图像即可根据三正交关系建立约束方程组,通过矩阵特征值分解,求得摄像机内参数的解析解.对同一个摄像机进行对比实验,本文标定结果与平面经典法标定结果的相对误差仅为1.3%左右,且仿真数据实验和真实图像实验的结果表明,该算法具有较高的标定精度和鲁棒性.     

Self-consistent solution of the Schrodinger equation insemiconductor devices by implicit iteration

A novel iteration scheme for the self-consistent solution of the Schrodinger-Poisson system in semiconductor devices is presented. The information from the eigenvalue problem is used to obtain a nonlinear Poisson equation that can be solved with the Newton method. The scheme has good stability properties and fast convergence. Examples are presented for the one-dimensional (1-D) calculation of quantized states in surface-channel and buried-channel MOS devices     

A relation between Liou's method and the fourth-order Runge-Kutta method for evaluating transient response

The fourth-order Runge-Kutta method is shown to be a special case of Liou's method of evaluating transient response for a linear time-invariant system. The eigenvalue problem is then the same for each method.     

Analysis of a parallel resistive plate medium [EM scattering]

A half-space composed of parallel resistive sheets is studied by formulating an eigenvalue problem to find the characteristic modes of the medium. Two equivalent formulations of the eigenvalue problem are presented. The first approach is analytical in nature and provides greater insight into the physical behavior of the material, while the second is numerical and applicable to a wider class of problems. The eigenvalue problem is solved via the Muller method to find the complex modal wavenumbers and field distributions within the resistive sheet medium. The mode-matching procedure is used to study the medium's reflection and absorption properties     

金属包层非均匀平板介质波导传输特性分析

用微扰理论和多层分割法求得到金属包层非均匀介质波导导模的传播常数的一级和二级近似解,与用复本征方程求得的精确解进行比较,给出了与精确值符合相当好的数值结果,结果表明微扰法是相当好的近似方法,二级近似结果对一级近似结果的修正很小,一级近似已可以给出足够精确的结果。     

Some Properties of T-Septum Waveguides

Equations and curves giving cutoff frequency and impedance are presented for rectangular waveguide having a T-septum on one or both sides. It is shown that the T-septum waveguide has a lower cutoff frequency and wider bandwidth than a ridged waveguide of the same gap parameters. The impedance characteristic is shown to be almost the same as that of the ridged guide. Equations and charts are presented to facilitate the design of T-septum waveguides. Experimental measurements show a good agreement with the theoretical predictions. The theoretical results are obtained by the formulation of an integral eigenvalue equation which is subsequently solved numerically by application of the Ritz-Galerkin method. The eigenvalue spectrum is also discussed.     

非高斯有色噪声中谐波恢复的累积量投影方法

本文研究非高斯有色噪声中的谐波恢复问题。首先建立了复数线性非高斯过程的高阶累积量投影定理。应用该定理，由含噪谐波信号的四阶累积量求得非高斯有色噪声的自相关，然后通过求解一个广义特征值问题对矢量空间进行预白化，最后结合噪声子空间方法ＭＵＳＩＣ恢复谐波信号参数。本文方法克服了以往的困难，成功地解决了对称分布非高斯噪声背景下和谐波信号中存在二次相位耦合时的谐波恢复问题。仿真实验验证了本文结论。     

Determination of the resonant frequencies in a complex cavity usingthe scattering matrix formulation

A method for computing the resonant frequency in a complex cavity consisting of a series of waveguide sections is derived. The analysis is restricted to transitions in which one waveguide is wholly contained in the other. An eigenvalue problem is formed by cascading the scattering matrix from a given section outwards to the ends of the complex cavity, with appropriate boundary conditions at the ends. The eigenvalue equation is solved numerically by searching for a complex frequency, the cavity Q being determined by half of the ratio of the real to the imaginary part of the frequency. The technique is easily implemented numerically and shows good agreement with experiment. This method is suitable for modeling both abrupt changes in radius and smoothly varying tapers     

Modeling of the dielectric logging tool at high frequencies: theory

The high-frequency dielectric logging tool is analyzed, using first-principle electromagnetic field analysis, to determine characteristics such as tool behavior during measurement in a well logging environment. The theoretical model, a composite boundary value problem, consists of a source backed by an infinite ground plane (the measurement tool) in front of a two-dimensional inhomogeneity (geologic formation) which is divided into regions. The solution in each region is treated analytically in two dimensions, and numerically in one dimension. The one-dimensional problem is solved using the finite-element method, resulting in a conventional eigenvalue problem. This allows the eigenmodes of each region to be found systematically. Once the eigenmodes are found in each region, the solution for the two-dimensional inhomogeneity is obtained by matching boundary conditions at a discontinuity as in the method of mode matching. This gives the reflection and transmission operators characterizing each discontinuity     

On a Class of Electromagnetic Wave Functions for Propagation Along the Circular Gyrotropic Waveguide

The properties of confluent hypergeometric functions as exact electromagnetic wave fnnctions for propagation in a circular waveguide containing azimuthally magnetized remanent ferrite are investigated. Two different forms of solutions of the propagation problem for angular symmetric transverse electric modes are constructed-one in terms of Kummer and Tricomi confluent hypergeometric functions of complex parameter and variable and a second in terms of Whittaker functions. An evaluation of this class of wave functions is performed to sufficient extent, followed by tabulation of their imaginary zeros, providing computation of eigenvalue spectrum and phase characteristics of the gyrotropic guide.     

径向非均匀圆柱介质波导本征值问题的网络分析

用微波网络方法求解径向任意介质分布圆柱介质波导的本征值问题。利用阶梯近似,将径向非均匀介质波导的电磁场边值问题等效为多层耦合径向传输线网络的特征解问题,从而大大简化了求解过程,文中比较了本方法与其它方法的计算结果及有关测试值,表明本方法具有简单、精确和通用的特点。     

Efficient finite element analysis of waveguides with lossyinhomogeneous anisotropic materials characterized by arbitrarypermittivity and permeability tensors

This paper presents a new finite element formulation for solving arbitrarily shaped waveguides including lossy inhomogeneous anisotropic media. The materials are characterized by simultaneous [ε] and [μ] full tensors. Complex-mode computation, spurious-mode suppression and the possibility of specifying the frequency as an input parameter are also achieved. The formulation leads to a quadratic eigenvalue problem of dimension N which is transformed into an efficient 2N-dimensional generalized eigensystem with sparse complex matrices. This eigensystem is solved by the subspace method, taking full advantage of the sparsity of the matrices. Permittivity and permeability tensors with some null terms allow an additional reduction from the N-dimensional quadratic eigenvalue problem to a N-dimensional sparse complex generalized eigensystem. The proposed method has been validated by analyzing different lossy, inhomogeneous and anisotropic waveguides. Results show good agreement with previously published data     

On Slow-Fading MIMO Systems With Nonseparable Correlation

In a frequency-selective slow-fading channel in a multiple-input multiple-output (MIMO) system, the channel matrix is of the form of a block matrix. A method is proposed to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. Asymptotic eigenvalue distribution of is also calculated, where the entries of are jointly Gaussian, with a correlation of the form (where is fixed and does not increase with the size of the matrix). An operator-valued free probability approach is used to achieve this goal. Using this method, a system of equations is derived, which can be solved numerically to compute the desired eigenvalue distribution.     

Solution of the nonlinear eigenvalue boundary-value problem for tm electromagnetic waves propagating in a Kerr-nonlinear layer by means of the cauchy problem method

The problem of propagation of TM electromagnetic waves in Kerr-nonlinear layer is considered. The problem is reduced to the solution of a nonlinear eigenvalue boundary-value problem for a system of two ordinary differential equations. A numerical method is proposed for solving the considered eigenvalue boundary-value problem. It is shown that the proposed method makes it possible to investigate more complicated types of nonlinearity. Numerical results are reported. The method is compared to another known technique and to the linear case.     

An efficient finite element formulation to analyze waveguides withlossy inhomogeneous bi-anisotropic materials

In this paper a finite element formulation in terms of the magnetic field is presented for the analysis of waveguides with bianisotropic media. Such a formulation can deal with lossy inhomogeneous materials characterized by simultaneous permittivity, permeability, and cross-coupling (as in optical activity) arbitrary full tensors. The analysis takes into account arbitrary cross sections, and results in spurious-mode suppression, complex-mode computation, and the possibility of alternatively specifying the frequency or the complex propagation constant as an input parameter. In this way, many novel classes of waveguides with promising applications, such as chirowaveguides and chiroferrite-waveguides, can be analyzed. The formulation leads to a quadratic sparse eigenvalue problem which is transformed into a sparse generalized eigenvalue problem. This eigensystem is solved by the subspace method, the sparsity of the matrices being fully utilized. The proposed method has been validated by analyzing waveguides with biisotropic and bianisotropic materials. The agreement with previously published data is found to be excellent