Spectral Logic and Its Applications for the Design of Digital Devices
Spectral Logic and Its Applications for the Design of Digital Devices
复制标题
谱逻辑及其在数字设备设计中的应用
DOI：
10.1002/9780470289228
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
J. Astola
中科院分区：
文献类型：
--
作者：
M. Karpovsky;R. Stankovic;J. Astola
前言。致谢。数字列表。表列表。ACRONYMS.1。逻辑功能。1.1离散函数。1.2离散函数的表格表示。1.3函数表达式。1.4离散函数的决策图。1.5逻辑函数的谱表示。1.6逻辑函数的定极性Reed-Muller表达式。1.7逻辑函数的Kronecker表达式。1.8逻辑函数的电路实现。逻辑函数的谱变换。2.1谱变换的代数结构。2.2傅立叶级数。2.3布尔函数系统的基。2.4 Walsh相关变换。2.5多值函数系统的基。2.6离散Walsh和vilenkin - chrestenson变换的性质。2.7自相关和互相关函数。2.8任意有限阿贝尔群上的调和分析。2.9有限非阿贝尔群上的傅立叶变换。谱变换的计算。3.1 Walsh谱的计算3.2 Haar谱的计算3.3 vilenkin - christensen谱的计算3.4广义Haar谱的计算3.5自相关函数的计算决策图优化中的谱方法。4.1决策图的尺寸缩减。4.2线性变换二值决策图的构造。4.3线性变换平面BDD的构造。4.4决策图的谱解译。逻辑功能的分析和优化。5.1布尔函数的谱分析。5.2阈值元网络的分析与综合。5.3逻辑函数的复杂性。5.4交换函数系统的串行分解。5.5交换函数系统的并行分解。逻辑网络合成中的谱方法。6.1组合器件合成的谱方法。6.2不完全指定函数合成的谱方法。6.3多值函数合成的谱方法。6.4数字函数和序列发生器的谱合成。序列机器的谱合成方法。7.1用谱方法实现有限自动机。7.2完全指定自动机的状态与输入的分配。7.3不完全指定自动机的状态分配。7.4分配问题的一些特殊情况。光谱方法的硬件实现。8.1基于ROM的光谱合成方法。8.2光谱方法的串行实现。8.3序列Haar网络。8.4 Haar级数串行实现的复杂性。8.5光谱合成方法的并行实现。8.6并行实现的复杂性。8.7有限域展开实现。光谱方法的分析和合成可靠的装置。9.1分析纠错能力的谱方法。9.2合成可靠数字器件的谱方法。9.3序列机器的纠错能力。9.4合成具有自纠错功能的容错自动机。9.5谱方法与经典方法的比较。数字系统测试的光谱方法。10.1通过验证Walsh系数进行测试和诊断。10.2功能测试、错误检测、10.3处理器的线性检查。10.4多项式计算中检错的线性检查。10.5多项式计算中最优线性检查的构造。10.6线性检查的实现和检错能力。10.7数值计算的检验。10.8最优不等式检查和纠错码。10.9用线性检查检测计算机内存中的错误。10.10用两个正交不等式定位rom中的错误10.11随机存储器错误的检测和定位。谱方法在逻辑函数上的应用和推广实例。11.1为特殊应用而设计的变换。11.2小波变换。11.3斐波那契变换。11.4二维频谱变换。11.5沃尔什变换在宽带无线电中的应用。附录a.参考文献。索引。
PREFACE. ACKNOWLEDGMENTS. LIST OF FIGURES. LIST OF TABLES. ACRONYMS.1. LOGIC FUNCTIONS. 1.1 Discrete Functions. 1.2 Tabular Representations of Discrete Functions. 1.3 Functional Expressions. 1.4 Decision Diagrams for Discrete Functions. 1.5 Spectral Representations of Logic Functions. 1.6 Fixed-polarity Reed-Muller Expressions of Logic.Functions. 1.7 Kronecker Expressions of Logic Functions. 1.8 Circuit Implementation of Logic Functions. 2. SPECTRAL TRANSFORMS FOR LOGIC FUNCTIONS. 2.1 Algebraic Structures for Spectral Transforms. 2.2 Fourier Series. 2.3 Bases for Systems of Boolean Functions. 2.4 Walsh Related Transforms. 2.5 Bases for Systems of Multiple-Valued Functions. 2.6 Properties of DiscreteWalsh andVilenkin-Chrestenson Transforms. 2.7 Autocorrelation and Cross-Correlation Functions. 2.8 Harmonic Analysis over an Arbitrary Finite Abelian Group. 2.9 Fourier Transform on Finite Non-Abelian Groups. 3. CALCULATION OF SPECTRAL TRANSFORMS. 3.1 Calculation of Walsh Spectra. 3.2 Calculation of the Haar Spectrum. 3.3 Calculation of the Vilenkin-Chrestenson Spectrum. 3.4 Calculation of the Generalized Haar Spectrum. 3.5 Calculation of Autocorrelation Functions. 4. SPECTRAL METHODS IN OPTIMIZATION OF DECISION DIAGRAMS. 4.1 Reduction of Sizes of Decision Diagrams. 4.2 Construction of Linearly Transformed Binary Decision Diagrams. 4.3 Construction of Linearly Transformed Planar BDD. 4.4 Spectral Interpretation of Decision Diagrams. 5. ANALYSIS AND OPTIMIZATION OF LOGIC FUNCTIONS. 5.1 Spectral Analysis of Boolean Functions. 5.2 Analysis and Synthesis of Threshold Element Networks. 5.3 Complexity of Logic Functions. 5.4 Serial Decomposition of Systems of Switching Functions. 5.5 Parallel Decomposition of Systems of Switching Functions. 6. SPECTRAL METHODS IN SYNTHESIS OF LOGIC NETWORKS. 6.1 Spectral Methods of Synthesis of Combinatorial Devices. 6.2 Spectral Methods for Synthesis of Incompletely Specified Functions. 6.3 Spectral Methods of Synthesis of Multiple-Valued Functions. 6.4 Spectral Synthesis of Digital Functions and Sequences Generators. 7. SPECTRAL METHODS OF SYNTHESIS OF SEQUENTIAL MACHINES. 7.1 Realization of Finite Automata by Spectral Methods. 7.2 Assignment of States and Inputs for Completely Specified Automata. 7.3 State Assignment for Incompletely Specified Automata. 7.4 Some Special Cases of the Assignment Problem. 8. HARDWARE IMPLEMENTATION OF SPECTRAL METHODS. 8.1 Spectral Methods of Synthesis with ROM. 8.2 Serial Implementation of Spectral Methods. 8.3 Sequential Haar Networks. 8.4 Complexity of Serial Realization by Haar Series. 8.5 Parallel Realization of Spectral Methods of Synthesis. 8.6 Complexity of Parallel Realization. 8.7 Realization by Expansions over Finite Fields. 9. SPECTRAL METHODS OF ANALYSIS AND SYNTHESIS OF RELIABLE DEVICES. 9.1 Spectral Methods for Analysis of Error Correcting Capabilities. 9.2 Spectral Methods for Synthesis of Reliable Digital Devices. 9.3 Correcting Capability of Sequential Machines. 9.4 Synthesis of Fault-Tolerant Automata with Self-Error Correction. 9.5 Comparison of Spectral and Classical Methods. 10. SPECTRAL METHODS FOR TESTING OF DIGITAL SYSTEMS. 10.1 Testing and Diagnosis by Verification of Walsh Coefficients. 10.2 Functional Testing, Error Detection, and Correction by Linear Checks. 10.3 Linear Checks for Processors. 10.4 Linear Checks for Error Detection in Polynomial Computations. 10.5 Construction of Optimal Linear Checks for Polynomial Computations. 10.6 Implementations and Error-Detecting Capabilities of Linear Checks. 10.7 Testing for Numerical Computations. 10.8 Optimal Inequality Checks and Error-Correcting Codes. 10.9 Error Detection in Computer Memories by Linear Checks. 10.10 Location of Errors in ROMs by Two Orthogonal Inequality Checks. 10.11 Detection and Location of Errors in Random-Access Memories. 11. EXAMPLES OF APPLICATIONS AND GENERALIZATIONS OF SPECTRAL METHODS ON LOGIC FUNCTIONS. 11.1 Transforms Designed for Particular Applications. 11.2 Wavelet Transforms. 11.3 Fibonacci Transforms. 11.4 Two-Dimensional Spectral Transforms. 11.5 Application of the Walsh Transform in Broadband Radio. APPENDIX A. REFERENCES. INDEX.