Orthogonal functionals of the Poisson process

In analogy to the orthogonal functionals of the Brownian-motion process developed by Wiener, ltô, and others, a theory of the orthogonal functionals of the Poisson process is presented making use of the concept of multivariate orthogonal polynomials. Following a brief discussion of Charlier polynomials of a single variable, multivariate Charlier polynomials are introduced. An explicit representation as well as an orthogonality property are given. A multiple stochastic integral of a multivariate function with respect to the Poisson process, called the multiple Poisson-Wiener integral, is defined using the multivariate Charlier polynomials. A multiple Poisson-Wiener integral, which gives a polynomial functional of the Poisson process, is orthogonal to any other of different degree. Several explicit forms are given for the sake of application. It is shown that any nonlinear functional of the Poisson process with finite variance can be developed in terms of these orthogonal functionals, corresponding to the Cameron-Martin theorem in the case of the Brownian-motion process. Finally, some possible applications to nonlinear problems associated with the Poisson process are briefly discussed.     

Space-Time Diversity Using Orthogonal and Amicable Orthogonal Designs

In this paper we consider the utilization of multiple transmitterand receiver antennas for space-time diversity. The optimalSNR scheme, which also provides the best diversity, is outlined.This scheme however involves a reduction in the data rate. Coding schemes are then presentedwhich not only achieve the optimal SNR but also mitigate the reductionof data rate. The proposed schemes are based on the theory of Orthogonal Designsand Amicable Orthogonal Designs.     

Network approximation of input-output maps and functionals

We give results concerning the problem of approximating the input-output maps of nonlinear discrete-time approximately finite-memory systems. Here the focus is on the linear dynamical parts of the approximating structures, and we give examples showing that these linear parts can be derived from asingle prespecified function that meets certain conditions. This is done in the context of an approximation theorem in which attention is focused on what we call basic sets. We also consider the related but very different problem of approximating nonlinear functionals using lattice operations or the usual linear ring operations. For this problem we give criteria, not just sufficient conditions, for approximation on compact subsets of reflexive Banach spaces (any Hilbert space is a reflexive Banach space).     

Estimating linear functionals of a PET image

The authors discuss the effect of having a finite number of detectors on the estimation of a bounded linear functional of a PET image. They argue that the functional should be estimated directly from the detector counts and give an estimate of the effect of the binning of the counts to order D(-2), where D is the number of detectors. The authors then suggest an estimator that includes a data determined bias correction reducing the bias to o(D(-2)).     

The theory of functionals of stochastic backscattered fields

The theory of wave scattering by anisotropic statistically rough surfaces, which is an important part of statistical radiophysics, is considered. A new analytic method is developed and generalized for solving problems of radar imaging. The method involves analytic determination of the functionals of stochastic backscattered fields and can be applied to solve a wide class of physical problems with allowance for the finite width of an antenna’s pattern. The unified approach based on this method is used to analyze the generalized frequency response of a scattering radio channel, a generalized correlator of scattered fields, spatial correlation functions of stochastic backscattered fields, frequency coherence functions of stochastic backscattered fields, the coherence band of a spatial-temporal scattering radar channel, the kernel of the generalized uncertainty function, and the measure of noise immunity characterizing radar probing of the Earth’s surface or extended targets. The introduced frequency coherence functions are applied for thorough and consistent study of techniques for measuring the characteristics of a rough surface, aircraft altitude, and distortions observed when radar signals are scattered by statistically rough, including fractal, surfaces. To exemplify urgent applications, radiophysical synthesis of detailed digital reference radar terrain maps and microwave radar images that was proposed earlier is considered and improved with the use of the theory of fractals.     

Lyapunov functionals for a class of wave equations

For a class of wave equations, a method of determining a suitable Lyapunov functional guaranteeing asymptotic stability is developed. The method is based on the construction of Lyapunov functions for ordinary differential equations. For a particular example, results identical to those determined from an eigenfunction expansion are obtained.     

基于正交脉冲的非正弦时域正交调制方法

针对非正弦波信号的频带传输问题,同时为了有效提高系统的频带利用率,提出了非正弦时域正交调制方法,基于频谱控制设计时域正交的正余弦脉冲组加载信息,已调信号是频谱特性可控的带限信号,在时域上正交,在频域上频谱相互混叠,接收端采用基于脉冲谐振的检测方法,可正确分离、检测信息.该调制方法有效提高了系统的频带利用率,且可适用于任意通信频段.     

正交特征群

本文在证明了有限Ａｂｅ１群Ｇ与它的特征群Ｇ√存在同构的一个必要充分条件之后，构造了一类正交特征群，从而概括了相当一大类正交变换（它包括了离散付里叶变换、阿达玛变换、数论变换、Ｃｈｒｅｓｔｅｎｓｏｎ变换）这对构成有限域与整环上的正交变换具有指导作用。     

A class of robust entropic functionals for image restoration

This paper considers the concept of robust estimation in regularized image restoration. Robust functionals are employed for the representation of both the noise and the signal statistics. Such functionals allow the efficient suppression of a wide variety of noise processes and permit the reconstruction of sharper edges than their quadratic counterparts. A new class of robust entropic functionals is introduced, which operates only on the high-frequency content of the signal and reflects sharp deviations in the signal distribution. This class of functionals can also incorporate prior structural information regarding the original image, in a way similar to the maximum information principle. The convergence properties of robust iterative algorithms are studied for continuously and noncontinuously differentiable functionals. The definition of the robust approach is completed by introducing a method for the optimal selection of the regularization parameter. This method utilizes the structure of robust estimators that lack analytic specification. The properties of robust algorithms are demonstrated through restoration examples in different noise environments.     

正交数字上变频器AD9857的应用

本文首先给出了正交数字调制器的应用场合与优点，然后介绍了AD9857的框图、性能、引脚及其功能，并讨论了AD9857的工作方式、数据输入、DDS核及DAC，阐述了AD9857的控制字及其读写控制，并给出了一个实际应用例子。     

Orthogonal code hopping multiplexing

An orthogonal code hopping multiplexing scheme is proposed as a statistical multiplexing scheme for an orthogonal downlink in order to accommodate more orthogonal downlink channels than orthogonal codewords for mobile stations, and its performance is evaluated.     

An Analytical Model of Iterative Interference Cancellation Receiver for Orthogonal/Orthogonal Overloaded DS-CDMA System

One of the efficient schemes to overload a CDMA system is to use two sets of orthogonal signal waveforms (O/O) Sari, Vanhaverbeke and Moeneclaey, IEEE Communication Magazine, 56–59, 2000. In this paper, we have presented the analysis of hard decision interference cancellation (HDIC) receiver for O/O overloaded DS-CDMA system. A closed form expression for the average bit error rate (BER) is obtained, for each stage of HDIC receiver, without considering the correlation between the multiple access interference and Gaussian noise. It is observed that at lower overloadings, analytical result matches closely to that obtained from simulation. But there is a difference between two at higher overloadings. The reason for such a difference is the inaccuracy in variance calculation due to the assumption of zero correlation. By using the Price’s theorem, we have obtained the correlation between tentative data decision and Gaussian noise samples. The overloading performance of a specific Quasi-synchronous sequence (QOS) O/O scheme is also evaluated using interference cancellation receivers.     

Orthogonal cycle transforms of stochastic matrices

In this paper we investigate new Fourier series with respect to orthonormal families of directed cycles , which occur in the graph of a recurrent stochastic matrixP. Specifically, it is proved thatP may be approximated in a suitable Hilbert space by the Fourier series . This approach provides a proof in terms of Hilbert space of the cycle decomposition formula for finite stochastic matricesP.     

M带余弦调制正交小波的设计

本文提出了一种M带余弦调制正交小波的设计方法。该方法将原型滤波器表示成一个满足K正则度条件的滤波器和一个待定滤波器的级联。并且优化的目标函数和约束条件都是优化参数的二次函数。从而简化了优化问题并获得了频率选择性更好的M带余弦调制正交小波。     

The Theory of Quaternion Orthogonal Designs

Over the past several years, there has been a renewed interest in complex orthogonal designs for their application in space-time block coding. Motivated by the success of this application, this paper generalizes the definition of complex orthogonal designs by introducing orthogonal designs over the quaternion domain. This paper builds a theory of these novel quaternion orthogonal designs, offers examples, and provides several construction techniques. These theoretical results, along with the results of preliminary simulations, lay the foundation for developing applications of these designs as orthogonal space-time-polarization block codes.     

正交法窄带噪声调制技术

通过对窄带随机信号的理论分析,利用窄带随机信号的经典表达式,提出正交法窄带噪声调制技术。采用该技术使调制后的窄带噪声谱质量在最大程度上逼近直放式窄带白噪声。经过试验证明,该技术是一种最佳的窄带噪声调制技术,并且可以方便地实现工程化。     

A new method of Lyapunov functionals for delayed cellular neural networks

Lyapunov functionals and Lyapunov functions coupled with the Razumikhin technique are still the most popular tools in studying the stability of large-scale retarded nonlinear systems. However, it is generally difficult to construct Lyapunov functionals or functions that satisfy the strong conditions required in the classical stability theory. We show that for some delay differential systems such as additive neural networks with delays, we can weaken the condition that the Lyapunov functional or function is positive definite, by using the equivalence between the state stability and the output stability. We apply our general theory to obtain some new stability conditions for cellular neural network models. It is represented that it is easy to construct Lyapunov functionals or functions satisfied conditions of our theorems.     

Orthogonal Matrices for Multi-Line Addressing

Simple orthogonal matrices are proposed to select multiple address lines simultaneously in RMS responding matrix displays. Good brightness uniformity of pixels can be achieved with less number of time intervals in an address cycle.