Spectral analysis of some independences on multiple-valued logical functions on their variables

There are many kinds of special relationships between multiple-valued logical functions and their variables, and they are difficult to be judged from their expressions. In this paper, some sufficient and necessary conditions of the independence and statistical independence of multiple-valued logical functions on their variables are given. Some conditions of algebraic independence of multiple-valued logical functions on some of their variables and the way to degenerate a function to the greatest extent are proposed, and some applications of these results are indicated. All the results are studied by using Chrestenson spectral techniques.     

SPECTRAL ANALYSIS OF SOME INDEPENDENCES OF MULTIPLE-VALUED LOGICAL FUNCTIONS ON THEIR VARIABLES

There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary conditions of the independence and statistical independenceof multiple-valued logical functions on their variables are given. Some conditions of algebraicindependence of multiple-valued logical functions on some of their variables and the way to de-generate a function to the greatest extent are proposed, and some applications of these resultsare indicated. All the results are studied by using Chrestenson spectral techniques.     

多值逻辑函数与其变元的几种无关性的谱分析

多值逻辑函数与它们的变元之间有许多种特殊关系,单从它们的表达式是较难判断的。本文给出了多值逻辑函数与其变元无关和统计无关的一些充分必要条件;给出了多值逻辑函数与其某些变元代数无关(也称为退化)的一些条件和最大程度地退化一个函数的方法;指出了这些结果在实际中的应用。所有这些结果都是Chrestenson谱方法来研究的。     

多值逻辑函数组构成置换的一个充要条件

本文给出了一组多值逻辑函数构成置换的一个充要条件。     

Using decision trees for the minimization of multiple-valued functions

This paper presents a simple procedure for the approximate minimization of multiple-valued functions using multiple-valued decision trees. The proposed procedure is compared with a near-absolute procedure, using for the test four-valued functions of four variables. The results show a great advantage for our procedure with respect to the CPU time needed.     

基于模代数的真值向量计算及其在多值逻辑综合中的应用

本文提出了由函数的真值向量计算Reed-Muller展式的简捷方法,由此可判定函数能否线性分解或部分线性分解。用典型例子演示了其在多值逻辑综合中的应用,结果表明该方法行之有效。     

Recursive two-dimensional spectral factorization

The factorization of two-dimensional spectral functions is a problem of interest in the digital processing of signals because of the nonexistence of a fundamental theorem of algebra for bivariate polynomials. In this paper we consider the special case of rational spectral functions, which are quotients of polynomials or pseudo-polynomials of finite order. We first characterize the general use of asymmetric halfplane factors, and then propose recursive procedures to obtain the factors. In the case of strictly positive spectral functions, we use the homomorphic transform to characterize the causal factor by its first-order data and then apply the modified leastsquares approximation to obtain the rational factors. For those cases of partially characterized spectral functions, we propose extensions of one-dimensional procedures. These alternative procedures are based on the modified least-squares approximation as well as on the two-dimensional Levinson algorithm. All the procedures presented are recursive, thus computationally efficient, and guarantee the stability of the factors in most cases.This work was supported by NSF Grant ECS-8105988.     

Circuit testable design and universal test sets for multiple-valued logic functions

The circuit testable realizations of multiple-valued functions are studied in this letter. First of all, it is shown that one vector detects all skew faults in multiplication modulo circuits or in addition modulo circuits, and n＋1 vectors detect all skew faults in the circuit realization of multiplevalued functions with n inputs. Secondly, min（max） bridging fault test sets with n＋2 vectors are presented for the circuit realizations of multiple-valued logic functions. Finally, a tree structure is used instead of cascade structure to reduce the delay in the circuit realization, it is shown that three vectors are sufficient to detect all single stuck-at faults in the tree structure realization of multiplevalued logic functions.     

Computational modeling of spectral data fitting with nonlinear distortions

Substances such as chemical compounds and biological agents are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Although spectra of pure substances can be identified by visual inspection, the spectra of their mixtures take a variety of complicated forms. Given the knowledge of spectral references of the constituent substances, the task of data fitting is to solve their weights, which usually can be solved by a least squares. Complications occur if the basis functions (reference spectra) may not be used directly to best fit the data. In fact, random spectral distortions such as shifting, compression, and expansion have been observed in some spectra. In this paper, we formulate mathematical model for such distortions and build them into data fitting algorithms. If minimal knowledge of the distortions is available, a deterministic approach termed augmented least squares is developed by fitting the spectral references together with their derivatives to the mixtures. If the distribution of the distortions is known a prior, we propose to solve the problem with maximum likelihood estimators which incorporate the distortions into the variance matrix. The proposed methods are substantiated with numerical examples including data from Raman spectroscopy, nuclear magnetic resonance, and differential optical absorption spectroscopy and show satisfactory results.     

A method to extend the spectral iteration technique

A method has been developed to extend the spectral iteration technique to encompass a more general class of subdomain type basis functions. While retaining the advantages of the spectral iteration technique, this method enables the usage of basis functions other than piecewise constant basis functions in expressing the unknown current distribution. Advantages of this technique with the choice of piecewise sinusoidal basis functions as compared to piecewise constant basis functions have been demonstrated for both antenna and scattering problems. This choice of basis functions is found to result in a further reduction in the number of unknowns required to represent the current distribution. Numerical results of the input impedance for a cylindrical antenna and the scattering cross section of a thin fiat plate are presented and discussed.     

光谱维编码中红外光谱成像系统的光学设计

基于双DMD提出了一种光谱维编码的中波红外光谱成像系统,利用空间维DMD完全补偿了光谱维编码DMD引起的像面倾斜。介绍了系统的组成和工作原理,设计了焦距为240 mm、F数为3的望远系统作为前置成像单元,采用双光路Offner光栅成像系统配合光谱维编码DMD同时实现了光线的色散、编码和合光等多个功能,设计了放大倍率为1的中继成像系统实现冷光阑匹配。通过整体优化设计实现了对双光路Offner光栅成像系统残余像差的补偿,设计结果表明,系统具有良好的空间成像和光谱性能,作用距离满足设计要求。     

嵌入式Web服务器下光谱成像技术研究

传统的光谱成像技术信息采集精度差,为了解决这一问题,研究了一种新的嵌入式Web服务器下的光谱成像技术,分析了光谱成像技术的工作原理,并根据光谱成像技术的信息获取方式和分光原理对其进行了科学的分类。通过移植嵌入式Web服务器不仅能够为光谱数据处理提供运行环境,还能够实现光谱成像技术的身份识别、马赛克光谱数据采集、图片预览、视频调焦等相关功能。在对采集的成像光谱的三维数据进行分析研究时,在Web服务器上实现图像维度的分离,完成定点元素维度的光谱信息获取技术。实验结果表明,该技术优化传统光谱成像技术预处理的算法,节省运算时间,减少成本,达到实时显示处理结果的效果,提高工作效率。     

On computing the spectral coefficients of a switching function

The spectral coefficients of a switching function are computed in terms of the real transform of the function, or equivalently, in terms of a disjoint sum-of-products representation of the function. Such a representation can be cast into an almost minimal form through some existing algorithms, and its complexity can be significantly less than that of a minterm expansion, which it includes as a special case. The real transform is also utilized as a mechanism for the inverse transform from the spectral domain to the Boolean domain.     

A spectral Integral method (SIM) for layered media

A spectral integral method is presented for electromagnetic scattering from dielectric and perfectly electric conducting (PEC) objects with a closed boundary embedded in a layered medium. Two-dimensional layered medium Green's functions are computed adaptively by using Gaussian quadratures. The singular terms in the Green's functions and the non-smooth terms in their derivatives are handled appropriately to achieve exponential convergence. Numerical results, compared with the ones obtained by using other methods, demonstrate the spectral accuracy and high efficiency of the proposed method. They also confirm that the spectral integral method (SIM) is applicable to concave objects.     

Parameter spectrum in spectral multiple-valued logic design

A Chrestenson transform over the p-valued logic domain is introduced. The parameter spectral coefficients, which consist of p parameters, from the transform are interpreted as measures of the dependence of the logic function on the linear logic functions. Six spectral operations and their applications to p-valued logic design are presented.     

Data-adaptive evolutionary spectral estimation

We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels     

Kullback-Leibler approximation of spectral density functions

We introduce a Kullback-Leibler (1968) -type distance between spectral density functions of stationary stochastic processes and solve the problem of optimal approximation of a given spectral density /spl Psi/ by one that is consistent with prescribed second-order statistics. In general, such statistics are expressed as the state covariance of a linear filter driven by a stochastic process whose spectral density is sought. In this context, we show (i) that there is a unique spectral density /spl Phi/ which minimizes this Kullback-Leibler distance, (ii) that this optimal approximate is of the form /spl Psi//Q where the "correction term" Q is a rational spectral density function, and (iii) that the coefficients of Q can be obtained numerically by solving a suitable convex optimization problem. In the special case where /spl Psi/ = 1, the convex functional becomes quadratic and the solution is then specified by linear equations.     

基于RM型三变量通用逻辑门的查表设计

本文讨论了逻辑函数的RM展开与分类，给出了基于逻辑函数RM展开的三变量函数P分类表、接线顺序表以及P分类代表函数的接线方案。在此基础上提出了基于RM型三变量通用逻辑门的查表设计方法，并给出了具体设计实例。     

Number of spectral coefficients necessary to identify a class of Boolean functions

It is well known that only n+1 spectral coefficients, the Chow or modified-Chow parameters, are necessary to uniquely define any given linearly separable (threshold) function. It is here shown that n+1 coefficients only are necessary to define a much wider class of Boolean functions, namely all Boolean functions which can be realised from a threshold-logic core function with pre- and postlinear-translation operations. The use of n+1 spectral coefficients as a fault signature for all such functions is therefore possible.     

Multiple-valued logic memory circuit

A new voltage-mode CMOS multiple-valued logic (MVL) memory circuit has been realized in a standard 2 μm p-well polysilicon-gate CMOS technology. This circuit requantizes MVL voltages during a setup clock mode and latches the input value during the hold clock mode. Using a 5 V supply and logical voltage increments of 1 -67 V, a quaternary memory circuit with a worst-case total setup and hold time of about 7 ns, and a best single-level transition total setup and hold lime of about 1 ns has been realized.