Residual Correlation for Generalized Discrete Transforms

We have undertaken a systematic investigation of the performance of a complete set of discrete orthogonal transforms Gr(n). The criterion of performance is that defined by Hamidi and Pearl, namely the Residual Correlation. This criterion measures the proportional correlation left in by a transform which is suboptimal, in the sense of not completely decorrelating the signal as in the case of the Karhunen-Loeve transform. The family of orthogonal transforms Gr(n), as defined by Ahmed and Rao, ranges from the discrete Walsh transform DWT, to the discrete Fourier transform DFT, as r varies from r = 0 to r = n - 1. Our study is applied to Markov-1 signals only.     

Energy Packing Efficiency for the Generalized Discrete Transforms

The concept of energy packing efficiency (EPE) of the Walsh-Hadamard transform (WHT) first proposed by Kitajima [1], is extended to other discrete orthogonal transforms. The concept as a criterion for evaluating the transforms is discussed. It is shown that the EPE is invariant for the generalized transforms as long as the ordering is the same.     

二维实值离散Gabor变换与DCT在图像编码中性能的比较

介绍了二维实值离散Gabor变换(RDGT)的快速算法,并着重探讨了二维实值离散Gabor变换与二维离散余弦变换在图像编码中的性能及差异.     

Discrete Sine and Cosine Transforms in Single Carrier Modulation Systems

In the DFT-based single carrier frequency division multiple access (SC-FDMA) modulation system, the discrete Fourier transform (DFT) is usually exploited to divide the frequency channel. In this paper, we propose to use discrete sine/cosine transforms in place of the DFT for SC-FDMA. Eight SC-FDMA systems based on various DST/DCT types are studied. The bit error rate (BER) and the peak to average power ratio (PAPR) are used to evaluate performance of these eight DST/DCT-based SC-FDMA systems in comparison with the conventional DFT-based SC-FDMA system in an AWGN environment. Simulation results show that the DST/DCT-based SC-FDMA systems with the use of localized FDMA scheme can provide better BER performance and yet keep the same PAPR performance as compared to the DFT-based SC-FDMA system.     

有限域上任意长度的DFT

有限域上的ＤＦＴ在数字信号处理，纠错码等领域都有重要应用。通常的有限域上ＤＦＴ仅限于长度与有限域特征互素的情形，它远远不能满足处理任意长度数据的需要。本文提出了有限域上任意长度的ＤＦＴ，研究了新变换的有关性质，并讨论了它在密码、编码中的应用。     

An Efficient and Privacy-Preserving Data Aggregation Scheme Supporting Arbitrary Statistical Functions in IoT

The Internet of Things(IoT) has profoundly impacted our lives and has greatly revolutionized our lifestyle. The terminal devices in an IoT data aggregation application sense real-time data for the remote cloud server to achieve intelligent decisions. However, the high frequency of collecting user data will raise people concerns about personal privacy.In recent years, many privacy-preserving data aggregation schemes have been proposed. Unfortunately,most existing schemes cannot support either arb...     

广义沃尔什函数的构造与生成

本文对沃尔什函数的对称复制和平移复制概念进行了推广,提出了用循环右移复制和广义平移复制方式来构造或产生广义沃尔什函数(Chrestenson函数)的方法     

非正交基函数与图象自适应表示

从算子理论的角度阐明了一给定信号用框架的有发子许愿安任意精度逼近；提出了基于非正交函数系的图像自适应表示算法，该中有效地表示新信号的局部特征及能量分布，作者以Ｇａｕｓｓｉａｎ基函数为例对二维图象进行了实验。     

Errors in Projection of Plane Waves Using Various Basis Functions

Basis functions play important roles in computational electromagnetics (CEM). It is interesting to investigate the errors in the projection of the equivalent current of a plane wave using various basis functions. In this work, the projection error of various basis functions is studied. The basis functions involved are the pulse basis function, the triangular basis function, higher-order versions of these basis functions, and the divergence-conforming basis function on rectangular and triangular elements. The projection errors are derived in closed form. The asymptotic expression of the closed form is given. The analytical results are verified by numerical results. The projection error of the pth order one-dimensional (1D) basis is asymptotically inversely proportional to the (p+1)th power of the density of unknowns. Based on the closed-form projection errors in the one-dimensional case, it is found that when the expansion basis is fixed, the application of different testing functions only affects the coefficient of the projection error, rather than the order. Generally, the error of the divergence-conforming basis in the projection of curl-free vectors is less than that of divergence-free vectors.     

Generalized Rational Function Approximation in Finite Intervals Using Zolotarev Functions

The results of Chebyshev in the theory of approximation find wide application in the design of circuits and microwave components. Part of the comparatively unknown work of Zolotarev and Achieser which has found useful applications in the design of certain microwave components, especially of mixed lumped/distributed components, is described. Several new results are presented, including formulas which enable the approximation functions to be computed in a relatively simple manner.     

Radiation patterns of an elliptical aperture in the Fresnel region

The Fresnel diffraction of a coherent light beam due to an elliptical aperture with the axial ratio (epsilon) between 1.0 and 0.5 is investigated. The computations are based on an procedure due to Hopkins. Perspective plots of the intensity distribution diagrams are generated for Fresnel number(F) = 5and the axial ratio(epsilon) = 1.0, 0.5, respectively. The results are compared with the corresponding diagrams for the circular aperture. With the decreasing axial ratio, it is observed that the central maxima and minima disappear in contrast to that of the circular aperture, whereas one finds a modulation in the central region along with the side maxima. Also given are the plots of the intensity distribution on the optical axis.     

Differential-Transfer-Matrix Based on Airy's Functions in Analysis of Planar Optical Structures With Arbitrary Index Profiles

A novel analytical method for solution of planar optical structure with arbitrary refractive index profile is proposed. This new method is founded on differential-transfer-matrices, whose field solutions are based on Airy's trial functions. In contrast to conventional Wentzel, Kramers, and Brillouin (WKB) solutions, which diverge around the turning points, this approach can be successfully used for exact calculation of various functions, including eigenvalues of optical waveguides with arbitrary index profiles, and complex reflection and transmission coefficients, even at the presence of turning points. The method is rigorous and can be applied for both major polarizations.     

Linear-Linear Basis Functions for MLFMA Solutions of Magnetic-Field and Combined-Field Integral Equations

We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can be mitigated by using the LL functions for discretization. This is achieved without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions     

基于RWG基函数的伽略金法中奇异性积分 的精确快速计算

利用电磁场积分方程的伽略金法求解理想导体电磁散射问题时需要计算奇异性的二重面积分(即4维积分).伽略金法的基函数和检验函数广泛采用RWG(Rao-Wilton-Glisson)矢量基函数.传统上采用奇异值提取技术和Duffy坐标变换法处理该奇异性积分,本文提出了一种更为精确和高效的计算方法,该新方法通过参数坐标变换、相对坐标变换、积分区域分解和广义Duffy坐标变换相结合的技术消除了被积函数的奇异性并降低了原4维奇异性积分的数值积分维数.通过计算实例证明该方法的精确性和高收敛特性.     

Application of the Characteristic Basis Function Method Utilizing a Class of Basis and Testing Functions Defined on NURBS Patches

A novel implementation of the characteristic basis function method (CBFM) is given, in which the high-level basis functions, called characteristic basis functions (CBFs), are represented in terms of curved rooftops generated from nonuniform rational B-splines (NURBS) in the parametric (u,v) domain. The associated macro-testing functions are defined by using curved razor-blade functions corresponding to each rooftop. The underlying objective of the CBFM is the reduction of the number of unknowns that arise from the discretization process when applying the conventional method of moments (MoM). The result is, therefore, an approach which can handle many complex cases via direct solvers, without suffering from convergence problems as many of the iterative techniques are known to do when dealing with ill-conditioned matrices. As a result of the combination of the CBFM with the special class of low-level basis and testing functions directly located over NURBS surfaces, complex and realistic geometries can be efficiently analyzed to yield accurate results while reducing the CPU time as well as required memory resources.     

广义同余神经网络中三种激励函数的比较研究

讨论了一种新的神经网络——广义同余神经网络（GCNN），阐述了它的定义和学习算法，并对GCNN中的三种激励函数进行了比较。算例表明，改进后的算法在学习速度和网络泛化能力上都有显著的提高。由于该神经网络易于操作和实行，有必要就相关理论及其应用作进一步的研究。     

广义严格雪崩准则及满足它的布尔函数性质

本文从实际出发减弱了Ｗｅｂｓｔｅｒ和Ｔａｖａｒｅｓ给出的严格雪崩准则（ＳＡＣ）的限制条件，定义了广义严格雪崩准则，并在不作出实质性“牺牲”的前提下避免了严格雪崩准则的阶数与非线性阶之间的折衷。同时，讨论了满足广义严格雪崩准则的布尔函数性质，结果表明满足严格雪崩准则的布尔函数具有的良好性质得到了很好的继承。     

任意实数阶复宗量第一类和第二类Bessel函数的精确计算

本文介绍了精确计算任意实数阶复宗量第一类和第二类Ｂｅｓｓｅｌ函数Ｊｕ（ｚ）和Ｙｕ（ｚ）的递推算法；给出了计算函数值时要用到的数学公式和典型数值计算结果，并对如何验证程序的正确性和分析计算结果的精度以及编程技巧作了较详细的讨论。