Paley定序法和Walsh定序法的Walsh变换方阵的一种算法

本文主要提出了Paley定序法和Walsh定序法的Walsh变换方阵的一种算法,并论述了它们的理论依据,建立了它们的直积关系式。     

Z[ω]环上的两类密码体制

本文在Eisenstein环Z[ω]上得到了两类新的密码体制。它们分别是推广的RSA密码体制和自确认密码体制。安全性分别基于环Z[ω]上整数的分解和Z[ω]环上离散对数的计算。     

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。     

基于TMS320C80的离散Walsh变换并行实现研究

针对离散Walsh变换(DWT)在实时信号处理中具有广泛应用,而其运算速度受到DSP器件性能限制的实际情况,进行了离散Walsh变换的并行性研究及并行性能分析;并在基于并行多处理机平台-TMS320C80的编程结构基础上,实现了并行离散Walsh变换。在TMS320C80进行的试验表明:所开发的并行DWT算法运行结果与理论分析是吻合的,该并行算法的速度和精度都得到了保证。     

“类整数DCT”变换快速并行算法的硬件实现

在分析"类整数DCT"变换基生成规则及其优越综合性能的基础上,设计了一种基于硬件流水线的"类整数DCT"变换快速并行算法的硬件结构,用加法和移位操作实现整数乘法。该设计结构简单、运算速度高、易于与微处理器系统接口,类整数DCT变换及其快速硬件流水算法的获得,为进一步降低视频编解码器的复杂度,提供了一个有价值的参考方案。     

支持同态算术运算的数据加密方案算法研究

针对在计算服务中,对用户信息加密以保护隐私时,无法对密文进行计算的问题,提出一种高效的支持密文四则算术运算的同态加密方案CESIL, 包括密钥生成、加密、解密及密文运算4个算法。该方案首先借助多项式环重新定义向量的加法和乘法运算,构建多项式系数向量环;然后利用理想格在向量环上划分剩余类,建立商环及其代表元集合;最后,将整数明文映射为代表元,并用代表元所在剩余类的其他元素替换该代表元,以对明文进行加密。商环的运算特性保证CESIL方案支持对密文的加法和乘法运算。在实现CESIL方案时,利用快速傅里叶变换(FFT)算法进一步提高运算效率、减少密钥长度。理论分析及实验结果表明,CESIL是语义安全的,且相比已有的一些同态加密方案,CESIL支持更多的运算类型,拥有较高的运行效率和较小的密钥及密文长度,能更好地满足实际应用需求。     

离散状态方程的序域解法

本文探讨了Walsh变换在时域离散系统状态空间分析中的应用。文中推广了Walsh变换的循环位移定理,并利用它对离散状态方程进行离散Walsh变换,导出了状态方程求解较为简便的公式,从而可以得到系统零状态响应的一组循环解。文末给出了数值计算实例。     

基于多通道体全息相关器的二维离散沃尔什变换

利用体全息相关器(VHC)可以完成多通道内积运算的特性,通过将待变换函数和二维沃尔什(Walsh)函数分别编码成输入图像和存储图像,提出了一种基于多通道体全息相关器的二维离散Walsh变换(DwT)方法.此方法可以快速、并行对输入函数做二维离散Walsh变换,并具有很大的速度提升潜力.利用散斑调制和随机交错方法可以提高运算精度.经验证,实验结果与理论值吻合.     

图像压缩编码中Walsh变换与DCT变换及其比较

图像变换是图像处理的基础,是图像压缩的第一步。在图像压缩中,DCT变换因其变换效果好而被广泛采用,成为目前最常用的图像压缩变换方法,而Walsh变换还未被广泛采用。通过对这两种变换的算法分析以及Matlab仿真实验和峰值信噪比的对比,结果表明,walsh变换在算法上比DCT简单,实现较为容易,其变换性能并不亚于DCT变换,在某些量化级上甚至还优于DCT变换,Walsh变换有着广泛的应用前景。     

有限域和剩余类环上非奇异反馈多项式的谱刻划

本文给出了有限域和剩余类环上非线性反馈移存器的非奇异反馈多项式及局部置换多项式的谱刻划，简化了素域上的现有结果，并对有限域上和剩余类环上相关免疫函数的谱特征给出了一个新的证明方法。     

Expansion of Walsh Functions in Terms of Shifted Rademacher Functions and Its Applications to the Signal Processing and the Radiation of Electromagnetic Walsh Waves

The expressions for Walsh functions in terms of shifted Rademacher functions are applicable to the design of a directive and selective array antenna for Walsh waves which is capable of eliminating the interference caused by impulsive noises. They also are applicable to voice processing because of their shift-invariant property. The shifted Rademacher functions were previously introduced by shiftiAg horizontally the periodic Rademacher functions. It was shown that the Walsh functions could be expressed as a linear combination of a finite number of the shifted Rademacher functions. This paper develops the actual expansions of the Walsh functions in terms of the shifted Rademacher functions. The coefficients in this series take only the values of either + 1 or -1. The shifted Rademacher coefficients appearing in the expansion of a given function in tenns of shifted Rademacher functions have the advantage that the coefficients of a shifted function are available by shifting cyclically the original coefficients.     

A New Walsh-Like Near Orthogonal (WNO) Sequence for Asynchronous CDMA System

Present generation mobile communication system employs one of the most popular wireless access technologies called code division multiple access (CDMA). Design of CDMA spreading codes has drawn significant attention amongst the researchers over the last few decades. CDMA code family is generally categorized into purely orthogonal and non-orthogonal (near-orthogonal) members which have established their application in synchronous (downlink) and asynchronous (uplink) CDMA system respectively. Walsh code has been regarded as the most useful spreading code to be used in synchronous link because of its orthogonality property. However, the performance of Walsh code is significantly inferior in asynchronous surroundings. A number of codes have consequently been proposed with an aim to mitigate the shortcomings of Walsh code. This paper makes an innovative attempt to enhance the correlation properties of existing Walsh code through one simple yet powerful algorithm. Proposed code of length ‘N’ has been generated from code sets of length ‘N/4’ and thus makes the code generation algorithm recursive in nature. Performance of the proposed code has subsequently been compared with some existing orthogonal and semi orthogonal codes in terms of various performance metrics and finally the supremacy of our proposition has been established.     

Relations among sequency, axis symmetry, and period of Walsh functions (Corresp.)

A parameter is defined that distinguishes the members of the set{WAL(s,m)}of Walsh functions. There is a one-to-one correspondence between sequency and axis symmetry of each Walsh function. Axis symmetry is derived from the sequency number. A procedure is introduced for obtaining the period of a Walsh function from its sequency number.     

Evaluation of data reconstruction using Walsh functions

The reconstruction of a finite-length record taken from a band-limited stochastic process is described. An integral mean-square-error criterion is used to compare the reconstruction using Walsh functions, a zero-order hold, and the sampling function (sin x)/x.     

Measurement of Continuous-Time Linear System Parameters Via Walsh Functions

The parameters of a continuous-time linear system are identified by use of an integral equation representation of plant-dynamics. Walsh functions are used to express the integral functions in terms of measured periodic output data. A simple method for numerical evaluation of the integral functions using matrices is given. Emphasis is placed on reducing computational requirements and in developing compact programs so that implementation on a 16-bit microprocessor is feasible. Computer simulations and experimental results obtained with a Texas Instrument 9900 microprocessor are used to discuss truncation errors, correction factors, and estimation accuracies.     

A Nonrecursive Equation for the Fourier Transform of a Walsh Function

Convolution of a discrete Walsh function with a rectangular pulse simplifies the derivation of an expression for the Fourier transform of a Walsh function. The nonrecursive transform equation that is developed is a function of the bits of the Gray code number for the order of the Walsh function.     

Walsh function approach for simplification of linear systems

A new approach for model order reduction of high order systems using Walsh functions is presented. The approach is based on minimizing the integral of the squared error between the impulse responses of the high order system and a low order model.     

沃尔什函数的一种新定义及其复制本质

利用有限Abel群的特征标理论，给出了沃尔什函数的一种新的定义方法，并阐述了沃尔什函数的正交特性和沃尔什函数的编号问题及其复制本质。     

Bandwidth requirements for Walsh functions (Corresp.)

The power-density spectrum for the Walsh function of binary orderkis calculated. The model analyzed considers the Walsh function as a random sequence modulating akth-order Rademacher function. The total number of Walsh functions of binary orderkand less is found to be aboutfrac{1}{6}of the overbound 2.4TW.     

Quasi-orthogonal sequences for code-division multiple-accesssystems

The notion of quasi-orthogonal sequence (QOS) as a means of increasing the number of channels in synchronous code-division multiple-access (CDMA) systems that employ Walsh sequences for spreading information signals and separating channels is introduced. It is shown that a QOS sequence may be regarded as a class of Bent (almost Bent) functions possessing, in addition, a certain window property. Such sequences while increasing the system capacity, minimize interference to the existing set of Walsh sequences. The window property gives the system the ability to handle variable data rates. A general procedure of constructing QOSs from well-known families of binary sequences with good correlation, including the Kasami and Gold (1967) sequence families, as well as from the binary Kerdock code is provided. Examples of QOSs are presented for small lengths. Some examples of quaternary QOSs drawn from Family A are also included