关于卷积积分概念引入方法的讨论

卷积积分对于信号处理,控制理论和动态控制电路分析均具有重要意义,大学本科生在第2学期或第3学期学习电路原理对首次遇到卷积积分,此时他们的教学基础还比较薄弱,因此概念的引入必须考虑到学生的理解能力。但作为学生日后经常翻阅参考书,教材中对于卷积积分的引入又必须兼顾科学性。本文首先对于现行各种著名的《电路分析》和信号与系统》教材中关于卷积积分的引入方法进行了综述,并评价了各种方法的优劣,在此基础上提出了能够比较好地解决科学性和易理解性矛盾的卷积积分概念引入方法。     

卷积码的Matlab仿真及其性能研究

信道编码是数字通信系统中的重要组成部分,他是保证信号可靠传输的一种重要方式。卷积码以其优越的性能被广泛使用在数字通信系统中。(2,1,7)卷积编码已经是国际卫星通信的标准。介绍了卷积码的特点以及卷积码的编码、译码原理,主要讨论了卷积码的Viterbi译码及其算法,最后通过Matlab仿真,对卷积码的性能进行了理论分析和实验仿真。     

On the Prandtl Equation

The unique solvability of the airfoil (Prandtl) integro-differential equation on the semi-axis ⁺ = [0, ) is proved in the Sobolev space W _p ¹ and Bessel potential spaces H _p ^s under certain restrictions on p and s.     

A recursive design methodology for VLSI: Theory and example

A novel VLSI (Very Large Scale Integration) methodology based on the hierarchical design of computational and system blocks is presented. The underlying algorithms used are shown to optimise the area-time complexity (AT²) of the computational units and at the system design level. The technique is illustrated for a matrix-matrix multiplication by using an image processing window convolver. This paper describes the performance of the recursive design technique comparing it to a typical systolic array, and demonstrates how data word size and convolution size may be expanded by movement up the architectural hierarchy. A prototype CAD (Computer Aided Design) autolayout program is described which maps directly into the hierarchical design environment. Using such design aids, flexible and correct designs may be generated which offer very simple data flow and highly local interconnection, with high performance.     

关于Montgomery的一个问题

本文解决了Ｍｏｎｔｇｏｍｅｒｙ提出的一个问题．     

Flexibility in the length of convolutions computed using Fourier-like fast transform algorithms

An efficient method of achieving flexibility in the length of discrete convolutions, computed using Fourier and Fourier-like fast transform algorithms, is described. Then this method is extended to discrete multidimensional convolutions computed using polynomial transforms.     

Tail Calculus with Remainder,Applications to Tail Expansions for Infinite Order Moving Averages,Randomly Stopped Sums,and Related Topics

We derive asymptotic expansions for tails of infinite weighted convolutions of some heavy-tailed distributions. Applications are given to tail expansion of the marginal distribution of ARMA processes, randomly stopped sums, as well as limiting waiting time distribution. AMS 2000 Subject Classifications. Primary—62E99, Secondary—41A60, 44A35, 60G50, 60K25     

Lévy–Khintchine Formula and Dual Convolution Semigroups Associated with Laguerre and Bessel Functions

In this work we consider a system of partial differential operators D ₁,D ₂ on K=[0,+[×R, whose eigenfunctions are the functions (x,t), (x,t)K, =((R0)×N)(0×[0,+[), which are related to the Laguerre functions for ((R 0)×N)(0,0) and which are the Bessel functions for (0×[0,+[). We provide K and with a convolution structure. We prove a Lévy–Khintchine formula on K, which permits us to characterize dual convolution semigroups on .