分布参数神经网络与偏微分方程求解

本文提出了一类用于求解偏微分方程的分布参数神经网络，并且在连续时空上研究了它的动态特性。最后还给出了两个模拟试验，用于检验这类网络的有效性。     

利用子波变换检测瞬时信号

本文提出一种基于子波变换的检测瞬时信号的方法。推导出一种适合于检测瞬时信号的子波基函数，并将其应用于检测波形和到达时间未知的瞬时信号，利用子波的伸缩和时移特性，通过对信号做多尺度的子波变换，可以在低信噪比下很好地检测到信号，本文还推导了相应的检测统计量及其统计分布特性，理论分析和计算机模拟结果表明，本方法是有效的，是提高检测性能的一种新途径。     

微机械加速度开关动态特性分析

本文通过建立微机械加速度开关检测质量运动微分方程，利用数值分析方法对开关动态特性进行了分析，从而为微机械加速度开关的动态设计提供了理论依据。     

宽带泄漏信号自适应对消器的性能

自适应对消器可以有效地消除雷达发射机宽带泄漏信号对雷达系统本身的影响。本文依据环路模型建立了描述自适应对消器工作过程的随机微分方程,求得了随机微分方程的瞬态解及其统计特性。最后导出了衡量对消器性能的干扰对消比的理论公式。     

散焦图像的深度恢复方法综述

散焦图像的深度恢复是根据两幅散焦图像模糊程度不同的特点,从两幅散焦图像恢复场景的深度信息,该方法已成功应用于工业检测、医学和军事等领域。结合国内外相关进展,主要论述了被动式散焦图像的深度恢复的确定性方法、统计方法、正则化方法和偏微分方程方法,并且分析了四种方法的优劣性。     

数字图像处理中的偏微分方程方法

图像是获取信息的重要媒介,图像处理技术广泛用于人类生活及社会生产中.偏微分方程是一种数学分析方法,并且它的特性由扩散方向和扩散项决定,这一点对图像处理大为有利.本文综述了近年来受到广泛重视的数字图像处理中的偏微分方程方法.给出了偏微分方程在图像去噪、图像放大、图像分割、图像修复中主要算法的优势及不足,同时给出了我们的改进算法,并展示了实验结果.     

双旁瓣对消器的性能分析

对双旁瓣对消器的性能进行了详细分析，建立了描述该系统的线性随机微分方程，给出了权向量Ｗ（ｔ）的统计特性，导出了干扰对消比的准确表达式。     

线性特性在推导微分方程解中的应用

本文利用＂信号与系统＂课程中定义的线性特性和线性系统的微分特性的物理概念,求解线性时不变连续系统的数学模型—线性常系数微分方程在时间域的解的方法。该方法与传统微分方程的求解方法有所不同,避免了传统解法中物理意义不清楚,求解灵活性不够的缺点。它从微分方程的最简单形式出发,利用线性特性,推导出一般形式微分方程的解。     

瞬态检测理论的发展前景

摘要：瞬态检测理论是赵子尧教授近年提出的检测弱确知信号的新理论，它与传统的积分检测理论不同，利用弱确知信号在瞬态特征上有别于干扰的瞬态特性，经过列微分方程，从混合信号E(t)中消去弱确知信号建立起仅同混合测知信号E(t)有关的干扰微分方程，先解出干扰，进而用混合测知信号E(t)减去已算出的干扰值后恢复出受检信令。本文阐述了瞬态检测的理论基础，给出适合数字信号处理的数值算法。     

基于广义高斯分布的彩色图像空域隐写检测算法

揭示了彩色图像相邻像素差服从或2倍近似服从广义高斯分布，且均值为零的统计规律；指出了目前常用隐写作业模式一代替作业模式在图像隐写方面的本质弱点。同时，本文针对彩色图像的空域隐写提出了一种结合稳健性统计特性和易损性统计特性为一体的快速盲检测算法，该算法检测效率高，速度快，便于实用。     

高斯白噪声经过线性系统后等效带宽特性研究

以随机信号经过线性系统理论为基础,研究了加性高斯白噪声经过滤波器后的带宽特性、等效带宽特性以及两者的关系,推导了以低通滤波器为例的线性系统的带宽和等效带宽公式。分析结果表明,等效带宽是说明线性系统滤波能力的一个重要参数,简单的使用带宽参数代替噪声等效带宽参数将使线性系统输出噪声功率的计算值增加,从而导致系统输出信噪比偏低,影响系统抗噪或滤波性能的评价。     

Adaptive lattice bilinear filters

Two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem, thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple, but results in biased system models in the presence of measurement noise. The second is an approximate least-squares output error solution; the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method     

Study of an integral equation arising in detection theory

This paper considers the solution of a Fredholm equation occurring in detection theory problems. A solution procedure, based on solving differential equations with nonmixed boundary conditions, is described for the case when the kernel of the integral equation is known to be the output covariance of a linear finite-dimensional system excited by white noise. Solutions with discontinuities are considered.     

微弱信号混沌检测方法的抗噪性能研究

针对混沌检测算法中临界状态不易准确判定,相变判别可能受到噪声影响的问题,首先阐述了基于Duffing方程的微弱信号检测原理,然后对混沌检测算法中噪声对系统输出的影响进行了推导和理论分析,设计仿真实验对复杂噪声条件下混沌系统的检测性能进行了分析。理论分析和仿真实验都表明,混沌系统对各种噪声都具有良好的免疫力,可以应用于强噪声背景下微弱信号的检测。     

控制滞后的线性时滞系统的状态反馈镇定

研究具有控制滞后的线性时滞系统的状态反馈镇定,其设计过程只需解一个特殊的Ric cati方程。并且指出,系统的输出反馈镇定问题可以转化为系统的状态反馈镇定问题来解决。最后通过实际例子和计算机仿真图形论证了本方法的有效性。     

Convergence analysis of a continuous-time nonlinear LMS-type algorithm using stochastic calculus

In several applications least mean square (LMS) has served as a good tool for estimating the parameters of linear models but the success of continuous-time in nonlinear models has not reached its height. In this paper, we have developed a nonlinear continuous-time LMS type algorithm that estimates parameters of nonlinear systems considering the noisy input–output relationship. The nonlinear system has been assumed to be memoryless and an additive Gaussian noise component to the system has been assumed. The mean squared error between the true system output and the estimated output, when the estimated output is modeled using the same form of the nonlinear function as the original system but with the parameters unknown, is minimized using the gradient scheme with the expectation removed. The result is a least mean square algorithm for nonlinear systems. In particular, we have performed a convergence analysis of the continuous-time nonlinear LMS algorithm applied to nonlinear systems when the time step goes to zero. The resulting algorithm then behaves as a stochastic differential equation, and the standard methods of Itô calculus and Fokker–Planck theory are applied to obtain statistical properties of the mean and covariance evolution of the parameter estimates. Computer simulations corroborate the theoretical results.     

Suboptimal estimation of the parameters of discrete systems in the presence of correlated noise

Using an unbiased objective function and a fast algorithm which employs an iterative least-squares technique, consistent estimates are obtained for the parameters of a linear difference equation which describes a system having an output corrupted by correlated noise. The method is applied to a simulated process and compared with the generalised least-squares method.     

Analytical model for switching transitions of submicron CMOS logics

We propose a new analytical model for the switching characteristics of CMOS logics. Our new model, named the Switching Response of CMOS logic by Convolution approach (SRC), can successfully produce the output waveforms under any switching conditions with simple analytical expressions. SRC modeling is a process of transforming CMOS logic into a linear system. This model provides procedures to determine the transfer function and the driving function (input of linear system) of the linear system from given CMOS logic, and then an output waveform, expressed as a third-order equation, is obtained by the convolution of two functions. All parameters in this model are determined in a straightforward manner from given device characteristics and layout geometry without empirical or fitting processes and presimulations. In addition, a delay equation is developed based upon the SRC model. With this delay equation, the delay can be predicted within a few percent differences compared to SPICE simulation results for the wide range of input transition time and output loading capacitance     

On identification of certain nonlinear systems (Corresp.)

In the fields of communication and control there sometimes arises the problem of determining the characteristics of a time-invariant system from discrete records of its input and output during a limited interval of time, where the output data are contaminated with random noise. When this system is linear, we can use the convolution sum to obtain a characterization of the output as a linear combination of past inputs. Hill and McMurtry [4] showed that if we choose a Legendre binary noise sequence as input to a linear system, then the least squares approximation to the characterizing coefficients is expressible in a computationally feasible form, even when a large number of coefficients is involved. In this correspondence we characterize a nonlinear system by a generalization of the convolution sum and show that if we choose Golomb's maximal linear recurring binary-noise sequence [2] as input, then the least squares approximation to the characterizing coefficients is expressible in a computationally feasible form. Thus, the maximal linear recurring sequence occupies the same role in investigating certain nonlinear systems that the Legendre sequence occupies in investigating linear systems.     

Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier

We present a theoretical analysis and an experimental study of the statistical properties of the noise accompanying an optical pulse propagating in a nonlinear semiconductor optical amplifier. Several degrees of gain saturation corresponding to different levels of optical signal-to-noise ratios (OSNRs) are examined. We employ the Heun numerical procedure to ensure proper convergence to the Stratonovich solution of the multiplicative propagation equation. This algorithm takes also into account the effect of gain saturation due to the amplified spontaneous emission noise. Moreover, the multicanonical Monte Carlo algorithm is used to efficiently calculate the probability density functions (pdfs), including the tails, of the peak of a pulse which emerges at the output of a saturated semiconductor optical amplifier. The results are compared to the corresponding pdfs obtained in a linear amplification system (where the optical noise is additive and Gaussian) having the same gain and under identical OSNR levels. We demonstrate that the pdf of the saturated amplifier is shifted toward lower power levels and is narrower, or equivalently, the mean and variance for the saturated amplifier case are smaller. Also, the difference between the two configurations increases with the degree of gain saturation. The theoretical predictions are confirmed by a series of experiments in which the pdfs at the output of the linear amplification scheme and saturated semiconductor optical amplifier are measured for an optical pulse of /spl sim/ 70-ps duration.