关于广义自缩序列的最小周期

伪随机性是密钥序列的不可预测性的重要度量指标。通过选择适当的比特串并分析其个数的奇偶性,证明了广义自缩序列b(a_(k-1))和b(a_(k 1))的最小周期达到最大,即2^(n-1)。类似地,讨论若干类广义自缩序列的最小周期,如:b(a_(k-1) a_(k 2)),b(a_(k-2) a_(k-1)),b(a_(k-2) a_(k 2)),…等,在大多数情形下证明了它们的最小周期达到最大,即2^(n-1)。     

当差分方程的特征方程具有重根时,在时域内求离散系统零输入响应解的模式

线性时不变离散系统通常是用线性常系数差分方程描述的。差分方程的一般形式为式中a_(n-1)…a_0,b_m、b_(m-1)…b_0,是由系统决定的常数,且n≥m。在引入移序算子E后,上述差分方程可写为求系统的零输入响应,即e(k)=0时的响应时,上述差分方程表示成为齐次差分方程,即此齐次差分方程的特征方程为目前国内可以找到的有关《信号与系统》课程的教科书或参考书,以及笔者所见到的有关外文资料,在讨论用时域法求离散系统的零输入响应时,对特征方程具有不等根时解的模     

重模剩余类环的一一幂变换及其在保密通信中的应用

本文讨论在一类重模剩余类环上建立公钥密码体制的条件,主要结果是:设域F=GF(p),p为素数,f_1(x),f_2(x),…,f_3(x)是多项式环F[x]上两两互素的不可约多项式,deg f_i(x)=n_i,i=1,2,…,s。sum from i=1 to s(n_i)=n, 设f(x)=multiply from i=1 to s(f_i(x)),则deg f(x)=n。定义重模剩余类环F[x]/(f(x))的幂变换为σ_k:α→α~k(moddp,f(x)),α∈F[x]/(f(x)),k∈N,当且仅当k∈Z_q~*时,σ_k为F[x]/(f(x))的一一幂变换,这里q=[p~(n1)-1,p~(n2)-1,…,p~(ns)-1],Z_q~*表示整数模q的缩系。     

工程数学

0157.5关于几类图的L(3,2,大学学报图G的(自然科学版 2004060002·标号问题/邵振东(南京大学)I]曲阜师范一2004,30(3)一24一28L(2,l)一标号是一个从顶点集V(G)到非负整数集的函数则}了(:)一f(,)}全1.图G的L(2,1卜标号数久(G)是使得G有max{f(。):?任V(G)}二k的L(2,l)一标号中的最小数k.该文将L(2,l)一标号问题推广到更一般的情形即L(3,2,l)一标号问题,并得出了Kneser图、高度不正则图、Halin图的入3(G)的上界.参6(木)、.J尹1工、石f(x),使得若d(x,y)二1,则!f(x)一f(军)}全2;若d(x,y)二2,工程数学~~…     

开关函数的一个特性

在开关网络(包括移位寄存器)的分析和综合,数字系统的故障检测等问题中都要涉及开关函数与某一变元无关的条件,关于这个问题文章〔1〕〔2〕都给出一些判别条件。本文通过实例指出开关函数的一个特性,给出开关函数与某一变量无关的一个新的条件,并给出这结论的数学证明,在证明中对充分性给出两种方法。设f(x_1,x_2…,X_n)是定义在V_n(F_2)=GTF(2)×G_1F(2)×…G_1F(2)X…上的一个开关函数。称f(x_1,x_2,…,x_n)与x无关,如果f(x_1…,x_(i-1),o,x_(i 1),…,x_n)=f(x_1,…,x_(i-),1,x_(i ),…,x_i)Ax_1,…,x_(i-1),x_( 1),…,x_n,EGF_((2))我们定义f(x_1,x_2,…,x_n)的重量W_((f))为     

1985年上海铁道学院铁道运输自动化与通信专业硕士研究生入学试题及题解

试题名称:数字信号处理一、已知一因果序列,其偶部h_e(n)的Z变换为 H_e(Z)=(Z~4+1)/Z~2试求该因果序列.(10分) 二、某因果、非时变系统的差分方程为 y(n)-a·y(n-1)=x(n)-1/a·x(n-1)试求其幅频响应.(10分) 三、已知某系统当冲激响应为h(n)时,频率响应为H(e~(jω)),试求当冲激响应为(-1)~nh(n)时的频率响应??(e~(jω))(10分)     

SnO2掺杂ZnO-Nb2O5-TiO2微波介质陶瓷

研究了 SnO_2对 ZnO-Nb_2O-5-TiO_2陶瓷相结构和微波介电性能的影响。随 Sn 添加量的增加,晶相组成逐步从(Zn_(0.15)Nb_(0.30)Ti_(0.55))O2相转变为 ZnTiNb_2O_8相,相对介电常数 ?r减少,?f向负频率温度系数方向移动, 当 Sn 含量增加到0.20,?f可降至 9.8×10–6℃–1。当 SnO2的摩尔比 y 为 0~<0.08 时,形成完全固溶体,提高 Q·f 值;当 y>0.08,部分Sn 形成第 2 相,降低其 Q·f 值。当 y 为 0.08,在 1 150℃烧结,具有很好的微波介电性能,其 ?r为 50.3,Q·f 为 14 892GHz,?f为 25.12×10-6℃–1。     

bent函数和半bent函数的二阶非线性度下界

该文研究了形如f(x,y)的n+1变元bent函数和半bent函数的二阶非线性度,其中xGF(2n), yGF(2)。首先给出了f(x,y)的2n-1个导数非线性度的精确值;然后推导出了函数f(x,y)的其余2n个导数的非线性度紧下界。进而给出了f(x,y)的二阶非线性度的紧下界。通过比较可知所得下界要优于现有的一般结论。结果表明f(x,y)具有较高的二阶非线性度,可以抵抗二次函数逼近和仿射逼近攻击。     

关于Trick算法中有关迭代公式的讨论

在具有周期输入和稳态周期响应的非线性电路的机助分析中,Trick提出了著名的快速算法,其简单迭代法的迭代公式是 x_0~((f+1))=integral from n=0 to (f+1)T f(x,t)dt+x_0~((0)) (1)本文认为在进入稳态之前,式中的f(x,t)不是周期函数,并指出文献[2]中的两处疏忽。 一、问题的提出 文献[2]为了确立式(1),给出了如下证明:     

F2n中点集的线性不等式刻画

在分组密码的差分攻击中，为了利用计算机搜索最佳差分路径，人们将问题转换为其S-盒的差分分布表的最佳线性不等式逼近问题。确切地说，给定向量空间F₂ⁿ的一个非空点集A，寻找数目尽可能少的一次多项式的集合，使得满足所有多项式的值均大于或等于0的点集恰好为给定的点集A。在文献中能看到的做法通常是利用计算机软件(例如SAGE数学软件)算出很多的多项式，再用线性规划的方法从中挑选出最小个数的多项式。研究一次多项式的产生方法，称F₂ⁿ中的点集S是相容的，是指存在某个整系数一次多项式f(X)，使得S={P∈F₂ⁿ|f(P)<0}。主要有以下3个方面的结果：一是给定向量空间的维数n，对任意的1≤k≤2n，一定存在k元相容点集S；二是利用多项式加法的技巧，构造出一批k元相容点集；三是对于小参数k=1,2,3,4，给出k元点集S是相容的充分必要条件，同时也给出相应的k元相容点集的计数公式。     

Faster image template matching in the sum of the absolute value ofdifferences measure

Given an mxm image I and a smaller nxn image P, the computation of an (m-n+1)x(m-n+1) matrix C where C(i, j) is of the form C(i,j)=Sigma(k=0)(n-1)Sigma(k'=0) (n-1)f(I(i+k,j+k'), P(k,k')), 0=/相似文献   

An Efficient Algorithm for Computing the Reliability of Consecutive-$k$-Out-Of-$n$:F Systems

Many algorithms for computing the reliability of linear or circular consecutive-k-out-of-n:F systems appeared in this Transactions. The best complexity estimate obtained for solving this problem is O(k³ log(n/k)) operations in the case of i.i.d. components. Using fast algorithms for computing a selected term of a linear recurrence with constant coefficients, we provide an algorithm having arithmetic complexity O(k log (k) log(log(k)) log(n)+k^omega) where 2相似文献   

Decoding by linear programming

This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f/spl isin/R/sup n/ from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the /spl lscr//sub 1/-minimization problem (/spl par/x/spl par//sub /spl lscr/1/:=/spl Sigma//sub i/|x/sub i/|) min(g/spl isin/R/sup n/) /spl par/y - Ag/spl par//sub /spl lscr/1/ provided that the support of the vector of errors is not too large, /spl par/e/spl par//sub /spl lscr/0/:=|{i:e/sub i/ /spl ne/ 0}|/spl les//spl rho//spl middot/m for some /spl rho/>0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced in this paper improve on our earlier work. Finally, underlying the success of /spl lscr//sub 1/ is a crucial property we call the uniform uncertainty principle that we shall describe in detail.     

Novel application of generalised current conveyor

It is shown that the generalised current conveyor (characterised by the instantaneous terminal relations iy=h12ix, vx=h21vy and iz=h32ix) in conjunction with an activc-RC network derived from a given grounded immittance simulation network (i.e. 1-port with Y11=y(s)) can be used to realise the same type of immitance function in floating form (i.e. as a 2-port characterised by y11=?y12=?y21=y22=ky(s), k being a positive scale factor) with several advantages over earlier methods of floating immittance synthesis.     

Design of Feedforward Input for Output-Settling Control With Dual-Stage Actuators

The settling problem is an output transition problem, i.e., given an initial state x(0), the goal is to bring the output to a desired value y(t_f) = y macr and hold it constant after the end of settling, t > t_f. This article develops the direct solution to the optimal-output-transition (OOT) problem for settling, and develops a method to use postactuation inputs to optimize the settling cost. The approach is illustrated with simulations on an example dual-stage system model. Simulations are also used to illustrate the reduction in the computational burden for online implementation by using linear combinations of precomputed inputs.     

The Viterbi optimal runlength-constrained approximation nonlinearfilter

Simple nonlinear filters are often used to enforce “hard” syntactic constraints while remaining close to the observation data, e.g., in the binary case, it is common practice to employ iterations of a suitable median, or a one-pass recursive median, openclose, or closeopen filter to impose a minimum symbol runlength constraint while remaining “faithful” to the observation. Unfortunately, these filters are-in general-suboptimal. Motivated by this observation, we pose the following optimization: given a finite-alphabet sequence of finite extent y={y(n)}_n=0^N-1 , find a sequence x={x(n)}_n=0^N-1 that minimizes d(x,y)=Σ_n=0^N-1d_n(y(n), x(n)) subject to the following: x is piecewise constant of plateau run-length ⩾M. We show how a suitable reformulation of the problem naturally leads to a simple and efficient Viterbi-type optimal algorithmic solution. We call the resulting nonlinear input-output operator the Viterbi optimal runlength-constrained approximation (VORCA) filter. The method can be easily generalized to handle a variety of local syntactic constraints. The VORCA is optimal, computationally efficient, and possesses several desirable properties (e.g., idempotence); we therefore propose it as an attractive alternative to standard median, stack, and morphological filtering. We also discuss some applications     

On single-sample robust detection of known signals with additive unknown-mean amplitude-bounded random interference--II: The randomized decision rule solution (Corresp.)

A randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown-mean amplitude-bounded noise. The saddlepoint solutionphi^{0}uses an equaUy likely mixed strategy to chose one ofNBayesian single-threshold decision rulesphi_{i}^{0}, i = 1,cdots , Nhaving been obtained previously by the author. These decision rules are also all optimal against the maximin (least-favorable) nonrandomized noise probability densityf_{0}, wheref_{0}is a picket fence function withNpickets on its domain. Thee pair(phi^{0}, f_{0})is shown to satisfy the saddlepoint condition for probability of error, i.e.,P_{e}(phi^{0} , f) leq P_{e}(phi^{0} , f_{0}) leq P_{e}(phi, f_{0})holds for allfandphi. The decision rulephi^{0}is also shown to be an eqoaliir rule, i.e.,P_{e}(phi^{0}, f ) = P_{e}(phi^{0},f_{0}), for allf, with4^{-1} leq P_{e}(phi^{0},f_{0})=2^{-1}(1-N^{-1})leq2^{-1} , N geq 2. Thus nature can force the communicator to use an {em optimal} randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail.     

Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications

In this paper we present a unified way to determine the values and their multiplicities of the exponential sums Sigma_xisinF(q)zeta_p ^Tr(af(x)+bx)(a,bisinF_q,q=p^m,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial or p = 3,f=^x(3(k)+1)/2 where k is odd and (k,m)=1. As applications, we determine (1) the correlation distribution of the m-sequence {a_lambda=Tr(gamma^lambda)}(lambda=0,1,...) and the sequence {b_lambda=Tr(f(gamma^lambda))}(lambda=0,1,...) over F_p where gamma is a primitive element of F_q and (2) the weight distributions of the linear codes over F_p defined by f.     

Segmentation into three classes using gradients

Consider a three-dimensional "scene" in which a density f(x, y, z) is assigned to every point (x, y, z). In a discretized version of the scene the density D(i, j, k) assigned to the (i, j, k) th volume element (voxel) is the average value of f(x, y, z) over the voxel. Suppose that the points in the original scene can be meaningfully segmented into classes 1, 2, and 3 separated by two threshold values l and u. Partial volume artifact is the phenomenon that a voxel (i, j, k) which is at the interface of class 1 and class 3 (and thus contains only points with low and high densities) usually has a density D(i, j, k) between l and u, and so cannot be distinguished by density alone from a voxel which contains only points in class 2. We describe how a two-dimensional (gradient, density) feature space can be used for the segmentation of such discrete scenes into three classes in a meaningful way. We illustrate the method using examples from medical imaging.