Efficient Boundary Conditions for Bidirectional Propagation Algorithm Based on Fourier Series

Recently, we described a very simple but efficient bidirectional eigenmode expansion propagation algorithm based on Fourier series expansion for modeling optical field distribution in waveguide devices. In this communication, we report on the implementation of complex coordinate transformation into this algorithm as absorbing boundary conditions that greatly enhance the suppression of unwanted reflections from the boundaries of the computational window.      

平顶高斯光束通过硬边光阑传输算法的改进

用傅里叶级数和复高斯函数的乘积对硬边光阑的窗口函数进一步拟合,对平顶高斯光束通过硬边光阑光学系统的模拟算法作了改进,并给出了近似解析传输公式.对直接积分Collins公式和使用Wen方法的数值计算结果作了比较.研究表明,只要傅里叶级数项数不少于30,改进后的算法比直接用复高斯函数展开具有更高的计算精度.     

LFM信号的分数阶傅里叶域自适应滤波算法研究

对于线性调频信号(LFM)的滤波,采用处理平稳信号的方法对其滤波往往得不到很好的效果。本文利用了线性调频信号在分数傅里叶变换域上具有很好的时频聚焦性的特点,来实现信号在分数阶傅里叶域的自适应滤波,自适应滤波算法采用改进的步长LMS方法,对传统的LMS算法做出了改进,算法中步长处理中引入了一个限制因子,可以较好地解决算法收敛速度和稳态失调量之间的矛盾。仿真结果表明,此算法在处理分数阶域的LFM信号滤波比传统的LMS算法有较好的滤波效果。      

Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media

A multidomain pseudospectral time-domain (PSTD) method with a newly developed well-posed PML is introduced as an accurate and flexible tool for the modeling of electromagnetic scattering by 2-D objects buried in an inhomogeneous lossy medium. Compared with the previous single-domain Fourier PSTD method, this approach allows for an accurate treatment of curved geometries with subdomains, curvilinear mapping, and high-order Chebyshev polynomials. The effectiveness of the algorithm is confirmed by an excellent agreement between the numerical results and analytical solutions for perfectly conducting as well as permeable dielectric cylinders. The algorithm has been applied to model various ground-penetrating radar (GPR) applications involving curved objects in a lossy half space with an undulating surface. This multidomain PSTD algorithm is potentially a very useful tool for simulating antennas near complex objects and inhomogeneous media.     

A General Spectral-Domain Formulation of the Electromagnetic Scattering by a Perfectly Conducting Circular Cylinder

A full-wave method for the two-dimensional scattering problem by a perfectly conducting circular cylinder is presented, providing an exact solution for the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space spectral variable. This approach allows us to define an analytic continuation for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E and in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxial approximation is required. Extact expressions for the expansion coefficients are given, in terms of complex intergrations involving the Fourier spectrum of the incident beam.     

Combination of generalized admittance matrices in the form of poleexpansions

This paper describes a novel algorithm for the determination of the wide-band mathematical model of a waveguide component, segmented into elementary blocks of known characteristics. Starting from the Y-matrices of the blocks, given in the form of pole expansions in the frequency domain, the algorithm yields the overall Y-matrix in the same form. Therefore, it can be applied iteratively to find the pole expansion of the Y-matrix of larger and larger waveguide structures. The algorithm is particularly useful if the Y-matrix of the blocks are obtained by the boundary-integral-resonant-mode-expansion (BI-RME) method, which yields the Y-parameters just in the desired form. Two examples show that the joint use of the BI-RME method and of the algorithm described in this paper results in a very accurate and fast numerical code, well-suited for the wide-band modeling of complex waveguide structures     

离散傅里叶变换的算术傅里叶变换算法

离散傅里叶变换(DFT)在数字信号处理等许多领域中起着重要作用.本文采用一种新的傅里叶分析技术—算术傅里叶变换(AFT)来计算DFT.这种算法的乘法计算量仅为O(N);算法的计算过程简单,公式一致,克服了任意长度DFT传统快速算法(FFT)程序复杂、子进程多等缺点;算法易于并行,尤其适合VLSI设计;对于含较大素因子,特别是素数长度的DFT,其速度比传统的FFT方法快;算法为任意长度DFT的快速计算开辟了新的思路和途径.     

Wideband modeling of arbitrarily shaped E-plane waveguidecomponents by the “boundary integral-resonant mode expansionmethod”

The boundary integral-resonant mode expansion method is used for the solution of the eigenvalue problem involved in the determination of the poles and the residues of the Y-parameters of arbitrarily shaped E-plane waveguide junctions. Using this method, the frequency response and its sensitivity to deformations of the boundary can be calculated much faster than by other more conventional methods for arbitrary shapes. Therefore, the described algorithm is eligible for setting up very efficient CAD tools to produce optimized designs of complex E-plane components in reasonable times. Some examples demonstrate the efficiency of the method in the modeling of components of practical interest     

MATLAB环境下非线性控制系统的建模与仿真

MATLAB软件在许多科学领域中成为计算机辅助设计、算法研究和应用开发的基本工具,在MATLAB/Simulink中对线性定常系统或者简单的非线性控制系统的建模与仿真比较简单方便,但对复杂非线性控制系统的建模与仿真实现困难。提出一种在MATLAB环境下利用m函数实现非线性控制系统的建模与仿真方法,该方法简单直观,维护性较好,具有可移植性。对复杂的非线性控制系统的建模与仿真,该方法可以明显提高仿真的效率。仿真实例验证了该方法的有效性和可行性。     

Efficient Systolic Implementation of DFT Using a Low-Complexity Convolution-Like Formulation

A reduced-complexity algorithm is presented for computation of the discrete Fourier transform, where$N$-point transform is computed from eight number of nearly$(N/8)$-point circular-convolution-like operations. A systolic architecture is also derived for very large-scale integration circuit implementation of the proposed algorithm. The proposed architecture is fully pipelined and contains regular and simple locally connected processing elements. It is devoid of complex control structure and is scalable for higher transform lengths. It is observed that the proposed systolic structure involves either less or nearly the same hardware-complexity compared with the corresponding existing systolic structures. In addition, it offers eight times more throughput and significantly low latency compared with the others.     

FFT复数处理器设计与FPGA验证

本文介绍了一种基于现场可编程门阵列(FPGA)的快速傅里叶变换(FFT)复数处理器设计,可进行1024点复数计算。采用按时间抽取的基-4算法和基于RAM的蝶形结构。同时对最后一级旋转因子进行了优化,减少了存储器的资源占用。使用流水线的处理结构,控制器简单。最后定点matlab建模与Synopsys的仿真器VCS仿真结果进行了对比,功能正确。完成整个运算仅用了2064个周期。最后用Altera公司的Cyclone IV E系列EP4CE10E22C8芯片完成原型验证,在时钟频率为50MHz时,完成1024点复数FFT仅用41.28μs。     

LFM信号的一种最优滤波算法

本文提出了一种基于分数阶傅立叶变换的LFM信号的最优滤波算法.首先由线性最小均方误差估计的正交条件出发,得到了连续分数阶傅立叶域上的等效Wiener滤波算子的求解方法;在此基础上,进一步给出了滤波算子的离散化算法.分析及数值仿真的结果表明,这一算法不仅在性能上接近普通的Wiener滤波器,而且计算简单,便于实现.     

On the reciprocal of a Fourier series

The inverse or reciprocal of a complex periodic time function (expressed as a complex Fourier series) is another complex Fourier series. An algorithm for finding this inverse Fourier series is presented.     

A new subaperture approach to high squint SAR processing

A high squint subaperture (HSS) algorithm was developed from the perspective of a strip map synthetic aperture radar (SAR) system and has the ability to focus SAR data at extremely high squint angle of 55° with less than 1.27% mainlobe expansion or even higher squint angles if larger mainlobe expansion can be tolerated. The unique characteristic of this algorithm is that the subapertures are formed by multiplying the received signal with a set of overlapped complex conjugated reference signals where the chirp rate varies in the azimuth direction. This is done to solve the range focus problem that arises after the azimuth input signal undergoes the range walk removal procedure. As the IISS algorithm only involves short fast Fourier transforms (FFTs) and avoids interpolation, it is computationally efficient and allows for small data buffers and facilitates hardware real-time implementation. The distinct feature of this algorithm is its simplicity of implementation, which is vital in real time processing and motion compensation when the squint angle may be changing continuously     

Analysis and synthesis of an impedance-loaded loop antenna using the singularity expansion method

The singularity expansion method (SEM) is used to represent the current on a loaded loop antenna. The shift in the poles of the loop due to impedance loading can be analyzed using contour plots in the complex frequency plane of the Fourier modal impedance transfer functions. The same plot may also be used to determine a loading function which will yield a specified pole pattern leading to frequency or time domain synthesis. A simple example of time-domain synthesis is presented.     

改进的算术傅立叶变换（AFT）算法

算术傅立叶变换（AFT）是一种非常重要的傅立叶分析技术。AFT的乘法量少（仅为O（N））,算法结构简单,非常适合VLSI设计,具有广泛的应用。但AFT的加法量很大,为O（N∧2）,因此减少AFT的加法运算是很重要的工作。本文通过分析AFT的采样特点,给出了奇函数和偶函数的AFT的改进算法。然后在此基础上给出了一般函数的AFT的改进算法。改进算法比原算法的加法运算量降低了一半,因此计算速度快了一倍。本文改进的偶函数和奇函数的AFT算法还分别可以用来计算离散余弦变换（DCT）和离散正弦变换（DST）。     

NEW APPROACH TO ELECTROMAGNETIC SCATTERING FROM A CONDUCTIVE DISC-RING STRUCTURE

A one-dimensional modified integral equation for electromagnetic scattering from a metallic concentric disc-ring structure is derived by using Fourier expansion and separating the contribution of charge density from conventional EFIE. In the case of normal incidence, the derived equation is very simple and easy to be solved numerically regardless of the electric dimension of the structure. The comparison between the data of RCS of a disc by using this method and analytical method shows the effectiveness of this approach. Numerical results are also given for current distributions and the scattered fields for a disc-ring structure.     

Spectrum-estimation based lossless information recovery for?sparse array patterns

One of the open problems in lossless information hiding research is how to get adaptively better difference image architectures for given applications. In this paper we propose a simple and efficient approach to predict high-similar interpolation image from its sparse pattern and spectral expansion. After difference operator, peak value of the spike is very high. This method also provides a mathematic framework for evaluating de-correlating algorithm and can therefore be used to benchmark new algorithms. Finally, a proper reversible data hiding algorithm is also enclosed which refers conventional difference expansion principle. Overflow and underflow is considered in the fusion way. Simulations results demonstrate and verify that our new approach is much effective than local difference expansion method with good generalization performance.     

频谱互质重排亚奈奎斯特率采样方法

本文提出了一种基于频谱互质重排的超低速率信号采样方法.该方法将稀疏傅里叶变换从离散时间域拓展到连续时间域,首先通过互质结构傅里叶展开采样对频域稀疏信号的频谱分量进行重排和压缩,然后通过基于中国余数定理的亚线性算法对信号进行了重构.实验结果表明,本文所提的采样方法可进一步降低频域稀疏信号的采样速率.     

高斯束展开法的注记之二：简单支撑矩形换能器声场

进一步给出高斯束展开法的推广。将文献中的圆形函数的高斯函数展开作为已知的结果,通过傅里叶或贝塞尔变换,余弦函数也可表示成高斯函数的叠加。因而菲涅尔场积分可以简化成一系列简单的代数函数的求和。利用这一方法,计算了简单支撑矩形活塞换能器声场分布。与解析解的数值结果相比,结果相当一致。