一种计算一维Walsh变换的MIMD并行算法

本文给出了一种计算一维Walsh变换的MIMD并行算法。它结构简单、易使用且性能好。当变换长度为N(=2~n),可用处理机数为1/n,它具有约1/n倍加速及100％的处理机利用率。     

An Application of Walsh Functions in Radio Astronomy Instrumentation

Walsh functions can be used to advantage to perform phase switching in antenna arrays used for radio mapping of the sky by Fourier synthesis. This paper describes the reason for phase switching, the advantage of using Walsh functions, and the implementation of these ideas in the Very Large Array (VLA) program of the National Radio Astronomy Observatory.1     

Ordering of Walsh Functions

The construction of Walsh functions is derived by means of the concepts of "symmetric copy" and "shift copy." Recursive relations based on the Kronecker product of matrices are also deduced from these concepts. There is a fourth useful ordering of the Walsh functions, called here X-ordering, in addition to the three known orderings usually referred to as Walsh-, Paley-, and Hadamardordering. An X-ordering function has the following features: lower order numbers of X-ordering correspond to even functions; higher order numbers of X-ordering correspond to odd functions; even order numbers of X-ordering correspond to lower sequencies; odd number of X-ordering correspond to higher sequencies. Finally, relations between the four orderings are given.     

基于沃尔什函数的TIADC全数字校准算法

提出了一种校准时间交织模数转换器(TIADC)通道失配误差的全数字自适应后台算法.该算法利用沃尔什函数仅从TIADC的输出中调制产生伪杂散信号,可以重构出失配误差,并自适应地从TIADC输出中减去三个失配误差.所提出的技术的优势在于它只需要知道测量的输出信号和TIADC通道数,而无需任何其它信息,包括参考通道.同时针对...     

On Representations of Walsh Functions

A new recursive formula for defining Walsh functions on the real line is presented. It leads, in a natural way, to an explicit representation of Walsh futctions. The explicit representation can be identified with. the representation of Walsh functions by the products of Rademacher functions. It can also lead to other representations of Walsh functions in a straight-forward manner. Using the new-formulation, one can prove many known properties of Walsh functions easily and systematically and gain new insight.     

A Simple Recursive Definition for Walsh Functions

This paper presents a simple recursive definition for Walsh functions, which overcomes the shortcomings of other recursive definitions. A rule of thumb for writing down the explicit representation for Walsh functions of any order is also devised. In addition, this recursive formula is used to generate discrete Walsh functions in matrix form.     

Application of Walsh Functions for Microprocessor-Based Transformer Protection

The paper presents the application of Walsh functions for digital differential protection of power transformers. A digital differential relay impelementing the Walsh algorithm is simulated using a personal computer. The algorithm shows good response in terms of speed and accuray.     

cdma2000系统中Walsh码的优化分配算法

Walsh码是码分多址系统中一种重要的正交扩频码。随着 3G系统的发展 ,高速率数据业务的引入 ,对有限Walsh码资源的需求日益增加 ,因此合理的管理和分配成为必然。本文以cdma2 0 0 0系统中Walsh码的使用为例 ,分析了Walsh码的工作原理和使用现状 ,提出了一种动态分配的优化算法。     

Frequency Synthesis Using Walsh Functions

A new scheme for the programmable generation of either square or sine waves of a required frequency is proposed. It uses neither feedback, nor table lookup of stored values, but it derives the desired square wave from a Walsh function, fairly simple to select and to generate with digital circuits. For this purpose, the Walsh function is counted down in a binary counter, at whose output a function with clean spectrum results, whose spurious components can be bounded by a simple formula. This approach becomes the design principle for a programmable frequency synthesizer with phase-continuous output, practically instantaneous switching between frequencies, and no limit on the number of closely and evenly spaced frequencies that can be selected.     

Group Codes and Walsh Functions

The set of Walsh functions, wal(j,?), is the character group of the dyadic group. For O?j?2k it is shown that they may also be derived from the character table of the abstract Abelian group Ck generated by k elements of order two. The method uses Slepians modular representation table[3] to compute the 2k irreducible representations (each of degree one) of Ck. The character table, K, is a 2kx2k square array of +1's and -l's and, considered as a matrix, the orthogonality relationships for characters show that K has the Hadamard property, [K][K]T = 2K [I]. In fact, for the proper ordering of the group elements in the construction of the modular representation table it is the Hadamard matrix, the entries of whose ith row take on the values of the Walsh function wal (i,?) in each of ?/2k subintervals. In a similar way other permutations of the modular representation table define different functions taking on the values +l, -l, also orthogonal and in a one to one relationship to the Walsh functions. Since an n place binary group code with k information places is isomorphic to Ck,[3] each code can thus be used to generate real functions orthogonal over a given interval or period ?. In the special case of cyclic codes where the elements of the code interpreted as polynomials form an ideal in a polynomial ring of characteristic two, the group operation used in deriving the character table is of course, addition.     

Walsh Functions and Gray Code

Gray code is a natural way of ordering binary vectors in dyadic space, hence it appears frequently in connetion with Walsh functions. In Paley's definition of Walsh functions their sequencies are arranged in Gray code. Gray code also appears in a new Walsh function generation algorithm which obtains a function by locating all its sign changes. There are certain computational advantages in using Gray code rather than sequency ordering. Examples in fast Walsh transform, dyadic convolution and digital filtering are given. Methods of Gray code to binary conversion are discussed.     

Some Comments Concerning Walsh Functions

The use of explicit forms for Walsh functions removes much of the confusion surrounding these interesting functions and permits simple proofs of their properties. Thus, for example, their period is far easier to determine than Alexandridis found, but their Fourier spectra are more complex than Schreiber's approximation suggests. For wave-form analysis, certain Walsh functions--the regular symmetric square waves--are more useful than are the others.     

一种基于标准Walsh变换的改进SPIHT算法

在图像压缩领域,SPIHT被认为是目前最先进的嵌入式零树编码方法之一。利用SPIHT编码算法的优越性,结合Walsh变换的能够将矩阵能量向矩阵左上角集中的特点,提出了一种基于标准Walsh变换的改进SPIHT算法。仿真试验结果表明,在压缩比相同的情况下,算法的信噪比明显高于SPIHT算法信噪比。     

On Moments and Walsh Characteristic Functions

This correspondence treats the derivation of natural moments from their corresponding Walsh characteristic function via the dyadic derivative operator. The derivation of a result concerning Walsh transforms of dyadic derivatives of functions is also considered. However, some established ideas such as Walsh transform, dyadic stationarity, and dyadic correlation are introduced first.     

一种基于移位序列进行相关值计算的快速算法设计

该文针对以往传统的计算相关值算法,提出了移位序列分析法,得到了一种新的求相关值的算法。利用此法在理论上对相控序列的相关值进行了分析,得到的结果与原有结果是一致的,证明了该算法的正确性;在数值计算上对多种长度的序列进行了新老算法的比较,可以看出新算法非常快速地得出了结果。因此通过此法,既可以对已知的大量序列进行快速计算,从而得到有理想相关值的序列族;又可以很快捷地计算出将要构造的新序列的相关值,看其是否符合要求,从而判断其是否能够应用到相应的系统当中。     

离散傅里叶变换的算术傅里叶变换算法

离散傅里叶变换(DFT)在数字信号处理等许多领域中起着重要作用.本文采用一种新的傅里叶分析技术—算术傅里叶变换(AFT)来计算DFT.这种算法的乘法计算量仅为O(N);算法的计算过程简单,公式一致,克服了任意长度DFT传统快速算法(FFT)程序复杂、子进程多等缺点;算法易于并行,尤其适合VLSI设计;对于含较大素因子,特别是素数长度的DFT,其速度比传统的FFT方法快;算法为任意长度DFT的快速计算开辟了新的思路和途径.     

Walsh Orthogonal Functions in Geometrical Feature Extraction

Walsh functions are used in designinq a feature extraction algorithm. The ?axis-symmetry? property of the Walsh functions is used to decompose geometrical patterns. An axissymmetry (a.s.)-histogram is obtained from the Walsh spectrum of a pattern by adding the squares of the spectrm coefficients that correspond to a given a.s.-number ? and plotting these against ?. Since Walsh transformation is not positionally invariant, the sequency spectrum does not specify the pattern uniquely. This disadvantage is overcome by performing a normalization on the input pattern through Fourier transformation. The a.s.-histogram is obtained from the Walsh spectrum coefficients of the Fourier-normalized rather than the original pattern. Such histogram contains implicit information about symmetries, periodicities, and discontinuities present in a figure. It is shown that a.s.-histograms result in great dimensionality reduction in the feature space, which leads to a computationally simpler classification task, and that patterns which differ only in translations or 90° rotation have equal a.s.-histograms.     

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.