Design of IIR digital filters based on eigenvalue problem

This paper presents a new method for designing IIR digital filters with optimum magnitude response in the Chebyshev sense and different order numerator and denominator. The proposed procedure is based on the formulation of a generalized eigenvalue problem by using Remez exchange algorithm. Since there exist more than one eigenvalue in the general eigenvalue problem, we introduce a very simple selection rule for the eigenvalue to be sought for where the rational interpolation is performed if and only if the positive minimum eigenvalue is chosen. Therefore, the solution of the rational interpolation problem can be obtained by computing only one eigenvector corresponding to the positive minimum eigenvalue, and the optimal filter coefficients are easily obtained through a few iterations. The design algorithm proposed in this paper not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue. Some properties of the filters such as lowpass filters, bandpass filters, and so on are discussed, and several design examples are presented to demonstrate the effectiveness of this method     

A Linear-Time Complex-Valued Eigenvalue Solver for Full-Wave Analysis of Large-Scale On-Chip Interconnect Structures

This paper proposes a linear-time complex-valued eigenvalue solver for solving large-scale on-chip interconnect problems. The fast eigenvalue solution is achieved by eigenvalue clustering, fast system reduction with negligible computational cost, and fast linear-time solution of the reduced system. Numerical and experimental results are presented to demonstrate the accuracy and efficiency of the proposed method.      

基于极化联合特征值的雷达弱小目标检测方法

针对海杂波背景下雷达弱小目标检测问题,提出了一种基于极化联合特征值的雷达弱小目标检测方法。该方法利用多极化通道回波数据计算极化相干矩阵的最大特征值,然后将待检测单元的最大特征值与参考单元最大特征值、最小特征值、算数平均值和几何平均值的算数平均之比分别作为检验统计量实现检验判决。仿真和实测数据处理结果表明：基于极化联合特征值的雷达弱小目标检测方法较基于特征值的检测方法性能提高2 dB,较极化检测最优滤波器性能提高1.5 dB,较功率最大综合检测方法、SPAN检测方法性能提高5 dB,极化联合最大特征值-几何平均方法综合检测效果最好。     

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.     

Inferring the eigenvalues of covariance matrices from limited,noisy data

The eigenvalue spectrum of covariance matrices is of central importance to a number of data analysis techniques. Usually, the sample covariance matrix is constructed from a limited number of noisy samples. We describe a method of inferring the true eigenvalue spectrum from the sample spectrum. Results of Silverstein (1986), which characterize the eigenvalue spectrum of the noise covariance matrix, and inequalities between the eigenvalues of Hermitian matrices are used to infer probability densities for the eigenvalues of the noise-free covariance matrix, using Bayesian inference. Posterior densities for each eigenvalue are obtained, which yield error estimates. The evidence framework gives estimates of the noise variance and permits model order selection by estimating the rank of the covariance matrix. The method is illustrated with numerical examples     

Sensitivity of an eigenvalue of a multivariable control system

A formula for the evaluation of the sensitivity function of an eigenvalue is proposed. The result is arrived at by consideration of the problem of sensitivity of an eigenvalue of a linear multivariable time-invariant control system subjected to parameter variations.     

基于回归分析和主成分分析的噪声方差估计方法

准确可靠的噪声强度估计是数字图像处理领域中一个重要的研究课题。噪声估计的难点在于如何提取用于估计的纯噪声信息,近几年,许多算法采用主成分分析技术来避免图像纹理信息的干扰,用最小特征值来估计噪声方差,可以有效地减少图像纹理信息对估计结果的影响,所以这类方法对于高频图像(丰富纹理图像)效果很好。由于图像块数量有限,最小特征值实际上比真实噪声方差小,而且图像块数量越少,偏差越大。如果直接把最小特征值作为估计方差,则容易低估计高噪声。该文通过回归分析确定最小特征值跟真实噪声方差的比值和图像块数量呈幂函数关系,因此可以通过最小特征值和幂函数关系得到真实的噪声方差。实验表明该文方法既能处理高频图像,又适合各种噪声水平,同时也能处理乘性高斯噪声。     

Time Delay Estimation Method Based on Canonical Correlation Analysis

The localization of sources has numerous applications. To find the position of sources, the relative delay between two or more received signals for the direct signal must be determined. The generalized cross-correlation method is the most popular technique; however, an approach based on eigenvalue decomposition (EVD) is another popular one that utilizes the eigenvector of the minimum eigenvalue. The performance of the eigenvalue decomposition (EVD) based method degrades in low SNR and reverberation, because it is difficult to select a single eigenvector for the minimum eigenvalue. In this paper, we propose a new adaptive algorithm based on Canonical Correlation Analysis (CCA) to extend the operation SNR to the lower SNR and reverberation. The proposed algorithm uses an eigenvector that corresponds to the maximum eigenvalue in the generalized eigenvalue equation (GEVD). The estimated eigenvector contains all required information for time delay estimation. We have performed simulations with uncorrelated, correlated noise and reverberation for several SNRs, to show that time delays can be more accurately estimated (especially for low SNR) a CCA based algorithm versus the adaptive EVD algorithm.     

Evaluation of loss factor of multilayered inhomogeneous waveguidesfor magnetostatic waves using efficient finite element formalism

An efficient finite-element solution procedure is developed for calculating propagation losses of magnetostatic waves in multilayered inhomogeneous waveguides. The final matrix equation is reduced to a standard complex eigenvalue problem whose eigenvalue corresponds to the complex phase constant itself. Thus, iteration procedures are not necessary and the phase and attenuation constants can be directly obtained by solving a standard eigenvalue equation. The validity of the method is confirmed by calculating propagation losses of magnetostatic surface waves in a single yttrium-iron-garnet (YIG)-film structure. Numerical results for a triple-layered YIG film structure are also presented. It is found that, in the triple-layered structure, propagation losses are highly dependent on the linewidth of the film in which the magnetostatic potential is well confined     

Correction to the analysis of dielectric guides by transversemagnetic field finite element penalty function method with extensions

Recently a method to obtain the propagation constants of lossless dielectric waveguides using the Helmholtz equation with the finite element method and penalty function method was presented. The advantage of using this approach is that only one final eigenvalue matrix needs to be solved for only two components of the H-fields. We have determine that the results were obtained using an eigenvalue solver that did not account for the asymmetry in the final eigenvalue matrix. In this paper, we present the results of the same cases simulated using the correct eigenvalue solver, and the results obtained are in good agreement with previously published ones. We also show by simulation of appropriate cases, a high penalty factor is correlated to highly coupled modes, while weakly coupled modes may be correlated to small penalty factors. Finally, we have extended the penalty function method to include the complex case without the use of the perturbation method. The gain results obtained for a channel waveguide are in good agreement with previously published ones     

波导本征值问题的有限元分析

本文简要讨论了波导本征值问题的有限元分析方法。给出了一个用有限元法求解波导本征值问题的标准程序。使用该程序可以获得一大类横截面周界由直线及圆弧围成的波导的各个本征值和本征函数。文中通过对十几种不同结构波导本征值问题的求解,证实了该程序的可靠性。     

螺旋-圆柱波导系统特征值的研究

本文给出了螺旋-圆柱波导系统的特征方程,首次求得了此结构的复根模,推导出了实根模、虚根模和复根模相互之间的分界条件,并给出了一些特征值曲线。最后,利用特征方程近似计算了一个螺旋-圆锥喇叭天线的远场辐射方向图,数值结果与实验进行了很好的比较。     

A new ordering and grouping algorithm for the linear weighted group matched filter successive interference cancellation detector

A linear group-wise successive interference canceller in a synchronous code-division multiple-access system (CDMA) is considered in this paper. The proposed hybrid detector that combines successive and parallel cancellation techniques makes use of advantages offered by the two techniques. The convergence of the hybrid interference cancellation (HIC) detector is guaranteed by an adjustable parameter that depends upon the largest eigenvalue of the system's transition matrix. Since the largest eigenvalue is difficult to estimate, an upper bound is necessary for successful convergence. For this reason, a new upper bound for the maximum eigenvalue of the system's transition matrix was developed. Moreover, a new ordering and grouping algorithm that results in a higher convergence speed is proposed. Simulation results show that a significant improvement in performance is obtained using this technique.     

On the performance of the generalized sidelobe canceller incoherent situations

The convergence rate for the adaptive weights to reach the optimum value in an adaptive array system depends on the eigenvalue spread ratio of the autocovariance matrix. How the eigenvalue spread ratio in a generalized sidelobe canceller (GSC) is affected by the various parameters is studied. Expressions for the output power of the GSC in coherent situations are derived, and numerical results are included     

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.     

A feasible method to implement optimum CIR-balanced power control in CDMA cellular mobile systems

Power control is essential in the design of direct-sequence code-division multiple-access (DS-CDMA) techniques. Optimum power-control (OPC) methods with carrier-to-interference ratio (CIR) balancing have been formulated as eigenvalue problems for frequency-division/time-division multiple-access (FDMA/TDMA) cellular systems. For the CDMA cellular system, its OPC was also formulated as an eigenvalue problem based on a large link-gain matrix. The OPCs with CIR-balancing were realized by solving eigenvalue problems of link-gain matrices. We reformulate the CIR-balanced OPC in CDMA cellular systems by benefiting from the power constraints as an eigenvalue problem based on a novel link-gain matrix. For a feasible implementation, a two-level hierarchical power-control structure is proposed to carry out the eigendecomposition which is required for the CIR-balanced OPC. Shortages of unbalanced CIR and global outage are two common issues in CIR-balanced power control. To tackle these two problems, a simple linear prediction method and an adaptive on-off strategy are proposed. Furthermore, because of the capacity limitation of wireless communications, a differential pulse code modulation scheme is presented to reduce the number of bits required for the transmission of command words in the two-level hierarchical power-control structure.     

Eigenvalue/eigenvector assignment for multivariable systems and further results for output feedback control

The design procedure proposed by Srinathkumar and Rhoten for eigenvalue/eigenvector assignment is reinterpreted and its relationship to the matrix pseudoinverse is pointed out. An eigenvalue/eigenvector assignment method for output feedback control of nth-order n-input m-output (m?n) systems is also presented. Geometric interpretation of state-space equations readily shows how many, and which, elements of the closed-loop-system eigenvector or reciprocal basis vector can be specified.     

Modal characteristics of ferrimagnetic tridisk-coupled resonator

The eigenvalue characteristics of a ferrimagnetic tridisk-coupled (TDC) resonator are described first. A TDC resonator is made of three AlYIG ferrite disks partially scraped and mutually attached on a center conductor. The EM field is treated with a consistent theory. The eigenvalue characteristics computed with stress on the mode of ν=1 are represented by the Z₁₀ versus Z₀ and Z₁ versus κ/μ relationships, where Z₁₀ is a degenerate eigenvalue, Z₀ is a wavenumber-eccentric radius product, and Z₁ is a continuously varying eigenvalue dependent on κ/μ with a given value of Z₀. Z₁₀ is distinguished by either a single- or double-value region as a function of Z₀. The computed Z₁ versus κ/μ graph belonging to the double-value region demonstrates a contradiction to the physical reality, which is resolved by introducing an equivalent circular resonant mode. The equivalent resonant mode is definitely identified by a degenerate eigenvalue and its modal curve with large modal separation. Experiments were carried out with various center conductors. The experimental results support the equivalent resonant mode. Finally, discussions are presented     

Fast finite-difference time-domain analysis of resonators usingdigital filtering and spectrum estimation techniques

The use of digital filtering and spectrum estimation techniques for improving the efficiency of the FD-TD algorithm in solving eigenvalue problems is discussed. The great improvement of the efficiency of the method is demonstrated by means of both numerical and measurement results. In addition, several improvements to the present FD-TD method for eigenvalue analysis are presented. These include the analysis of open dielectric resonators and the extraction of the resonant frequencies from the FD-TD results. The result for the open dielectric resonator analysis is validated using measured data     

Numerical analysis of surface wave on microstrip antenna with lossysubstrate

The key to analysing a guided surface wave is to solve its eigenvalue equation. When the medium is dissipative, the eigenvalue equation is a complex transcendental equation. The Kuhn algorithm is applied to work out the eigenvalue equation