A technique for extracting the poles and residues of a system directly from its transient response

A novel approach for systematically deriving the complex poles and residues of a structure from a set of time-domain data is presented. The method is based on Prony's algorithm which involves the inversion of two matrices and a solution of the zeros of annth degree polynomial,nbeing the number of desired poles. Two numerical examples are presented and several numerical advantages of this method are discussed.     

Computation of exponentials in transient data

Prony's method is widely used to identify the poles of a time series. A numerical implementation of Prony's method based on the properties of the least-squares solution of the transient data matrices is described, and a practical indicator of the accuracy of the computational results that is based on the singular values of the transient data matrices is derived. This algorithm can be applied to time series which contain simple or multiple poles     

Breakdown voltage analysis of planar p-n junctions taking into account the radius of curvature of the corners in the patterning mask

The breakdown voltages of planar p-n junctions have been studied with respect to cylindrical or spherical junction curvature. However, in practical planar p-n junctions for high voltage, the radius of curvature of the corners in the patterning mask, which affects the actual three-dimensional junction curvature, must also be considered. A new simple one-dimensional numerical analysis method is proposed. For this method Poisson's equation has been reduced to a one-dimensional form in a polar coordinate system with two poles, and solved only for the surface of the depletion layer. To verify the method, an accurate three-dimensional numerical analysis for electrostatic potential distribution was also performed. Good agreement was found between the numerical breakdown voltages using this method and experimental data.     

Natural frequencies of circular disks

The natural frequencies or the singularity expansion method (SEM) poles are computed for circular disks. We treat the acoustically soft disk, i.e, the Dirichlet boundary condition, and the perfectly conducting disk. The poles are found by an application of theT-matrix method by searching the zeros of a determinant. The poles associated with the first values of the azimuthal indexmare shown in both cases, and numerical values are given in tables and figures. The internal resonances are also computed for the thin oblate spheroidal cavity and comparisons are made with the thin circular cylindrical cavity.     

空间目标的联合矩阵束极点估计

极点作为谐振区雷达目标的最主要电磁特性,具有很大的空间目标识别前景。但是在使用频域观测数据提取目标极点时,存在虚假极点和估计精度问题。针对上述问题,首先通过加窗和截断改进了后时响应信号的获取流程,抑制了虚假极点影响;然后采用最小描述长度法（MDL）估计极点个数,避免了定阶错误引起的虚假极点;最后采用联合矩阵束法估计极点,有效减少了单角度数据估计极点时存在的遗漏极点和虚假极点问题。FEKO软件验证表明,所提算法具有更高的精度和抗噪能力。     

Accurate modeling of line-defect photonic crystal waveguides

An accurate three-dimensional method to calculate the Bloch modes of photonic crystal (PhC) waveguides is proposed. Good agreement with available experimental and numerical data is obtained. The originality of the method lies in the fact that the Bloch modes are seen as the electromagnetic fields associated to the complex poles of an in-plane transversal scattering matrix. In comparison with previous approaches, the computational domain discretized is smaller and a higher accuracy for the losses of PhC waveguides is achieved.     

A simple procedure to eliminate known poles from a time series

An extremely simple procedure is presented for eliminating known or previously computed poles from a time series and for obtaining a `deflated' time series which contains only the remaining poles. Time-series deflation can be used in combination with any numerical algorithm used to compute poles. As an important example, it is demonstrated how the time-series deflation technique combined with Prony's method can produce more accurate results than the use of Prony's method alone     

目标电磁散射极点的不变性特征分析

对频域磁场积分方程在离散化的基础上进行了矢量分析，发现离散化后的矩阵方程中含有频率因子的算子矩阵仅包含了反映散射体形状的矢量信息，从而得出极点的分布只依赖于目标的外部形状信息这一结论；然后利用FDTD进行了仿真研究，从不同姿态角(散射方向)的后时响应数据中提取了极点，结果保持了较好的一致，进一步证实了目标姿态角的改变不会影响极点的分布这一特征。     

Impulse invariance and multiple-order poles

The impulse-invariant method of IIR digital filter design from a given analog filter is useful both in filter design and especially in discrete-time simulation of continuous-time systems. The article clarifies aspects of impulse invariance and, in particular, the handling of multiple-order poles. The user is currently faced with incorrect formulas and Matlab software. The problems are discussed, and a method valid for any order poles is presented via a numerical example using original Matlab code     

Computer-Aided Synthesis of Planar Circuits

This paper presents a fully computer-oriented iterative synthesis of an open-boundary planar circuit having an impedance matrix with prescribed poles and residues. A starting circuit pattern is given first, and it is represented by a finite number of parameters. Those parameters (and hence, the pattern) are then iteratively modified by using the Newton-Raphson method to realize the prescribed circuit characteristics. When the numbers of given poles and coupling ports are relatively small, the results are satisfactory both in the computing time and accuracy. Some numerical examples are given.     

背景噪声下的语音识别技术研究

研究了3种背景噪声下与说话人有关的孤立词语音识别方法。即语音前端声学处理法、正则相关分析的谱变换补偿方法和同模极点增加法。实验结果表明,这3种方法都有效地提高了噪声环境中语音识别率,其中较好的方法在强噪声环境中(信噪比为0 dB)的语音识别率达到80%以上,为信噪比较低的噪声环境中自动语音识别展现了美好前景。     

A Note on the Multiplicity of Poles in the Vector Fitting Macromodeling Method

Vector fitting is a robust macromodeling tool for rational approximation of spectral data obtained by full-wave electromagnetic simulators or high-frequency measurements. The technique iteratively calculates a suitable set of poles, and solves the residues of the transfer function in a two-step procedure. If poles with a higher order multiplicity occur during the pole-identification step, numerical problems and inaccuracies can result, especially if the normal equations are solved. This problem is illustrated on an RLC filter, and a generalization of the basis functions is proposed to resolve the issue     

一种雷达目标极点提取方法及极点特性的分析

散射物体复自然谐振频率(极点)是目标识别可以利用的一个重要特征。使用传统求解极点的方法,通常得到的极点数目比较多,并且存在TE、TM两种模式。因此,对极点的规律分析较多的是对其模式变化趋势的分析。这些特性对于极点的实际应用没有太大的意义。本文从频率矩量法得到的散射数据出发,提出了一种波形拟合的极点提取方法。以有限长柱和椭球为例。分析了极点与入射波模式、目标姿态的关系,得到有实际指导意义的结论。     

Coupling mechanism of two dipoles within a conductor-backed thindielectric slab above the earth

A coupling mechanism between two dipoles within a conductor-backed thin dielectric layer above the earth, suggested as subsurface interface CW radar transmitting and receiving antennas, is calculated by a saddle-point method. When the dielectric layer is thin enough to support a cutoff mode, the electric field at the point of receiving dipole due to a transmitting point dipole may be approximated by sum of contributions of branch points of TE mode and poles of TM mode. The branch points and poles contributions are interpreted as evanescent lateral-waves and leaky-waves, respectively. Comparison of numerical results and asymptotic results shows excellent agreement     

地下目标瞬态谐振特性研究

利用谐振特性实现目标辨识是雷达探测领域研究的热点问题之一,地下目标在电磁波照射下也会产生外部谐振现象,该谐振信号与媒质特性、目标固有特性有关。该文通过FDTD方法计算了地下目标的瞬态谐振特性以及损耗媒质参数对目标谐振信号的影响,利用极点展开方法(SEM)对计算结果进行了分析,在计算分析的基础上研究了利用谐振特性识别地下目标的可行性。结果表明:在一定条件下,利用目标的外部谐振特性可以识别地下目标。     

Selective observation of resonances via their ringing in transientradar scattering, as illustrated for conducting and coated spheres

Radar scattering amplitudes contain pole singularities whose importance was recognized in the context of the singularity expansion method. The scattering of impulsive signals, studied previously, was shown to involve a large number of such poles, whose residues combine to form creeping-wave pulses. It is shown here that the use of sinusoidal pulses of long but finite duration, with the carrier frequency tuned to a pole frequency, may selectively probe one pole at a time. The ringing of any such selected resonance may be viewed as a coherent superposition of a succession of long creeping-wave pulses. Illustrative numerical calculations are carried out for the example of conducting spheres with or without dielectric coating     

Pole extraction from real-frequency information

This paper describes a procedure, analogous to Prony's method, for extracting the complex-frequency poles of electromagnetic transfer functions. The method is refined mathematically and is applied to both electrical and mechanical test cases. The paper explains a multiple processing technique, involving the overlaying of several pole sets, by which redundant data are used to separate actual from curve-fitting poles. Identification of an unknown target by comparing its scattered field with the poles sets of known targets is also illustrated for simple targets.     

Numerical modeling of a spherical array of monopoles using FDTD method

In this paper, the spherical-coordinate finite-difference time-domain method is applied to numerical analysis of phased array of monopoles distributed over a sphere. Outer boundary of the given problem is modeled by accurate spherical-coordinate anisotropic perfectly matched layer. The problem of increased cell aspect ratio near the sphere poles causing degradation of results is solved by dispersion optimization through artificial anisotropy. The accuracy of the approach is verified by comparing a model case with an exact solution. Finally, radiation patterns obtained by frequency-domain near-to-far-field transform and s-parameters of the array elements are presented and validated by comparing with measurement data.     

A technique for approximating the location of surface- and leaky-wave poles for a lossy dielectric slab

An approximation technique for locating the surface- and leaky-wave poles for a lossy dielectric slab is presented. The problem is reduced to the simultaneous solution of two transcendental equations (for each of the perfect magnetic conductor (PMC) and perfect electric conductor (PEC) cases) which is shown to yield a simple approximate solution for the poles, and which can subsequently be refined using numerical optimization. The technique yields both surface-wave and leaky-wave poles, and results are presented for a typical example to demonstrate the approach. The greatest approximation accuracy was observed for surface-wave and leaky-wave poles well removed from the spectral gap. For poles either within or in close proximity to the spectral gap, an alternative iterative technique is proposed. Expressions for the number of proper plus improper surface-wave poles in a given problem are also derived.     

光滑目标表面不连续性极点分布规律研究

利用雷达目标散射场极点分布特征来进行目标识别具有重要的理论意义.用矩阵束法对导体球和圆柱体散射场进行极点提取,分析了当光滑导体球与圆柱体表面存在局部凸起和凹陷时,极点分布的变化规律.结果发现,当光滑导体球和圆柱体局部存在凸起时,和无凸起情况相比,极点的虚部变小;当光滑表面存在局部凹陷时,极点虚部变大.