Book description
Spectral techniques facilitate the design and testing of today's increasingly complex digital devices
There is heightened interest in spectral techniques for the design of digital devices dictated by ever increasing demands on technology that often cannot be met by classical approaches. Spectral methods provide a uniform and consistent theoretic environment for recent achievements in this area, which appear divergent in many other approaches. Spectral Logic and Its Applications for the Design of Digital Devices gives readers a foundation for further exploration of abstract harmonic analysis over finite groups in the analysis, design, and testing of digital devices. After an introduction, this book provides the essential mathematical background for discussing spectral methods. It then delves into spectral logic and its applications, covering:
Walsh, Haar, arithmetic transform, Reed-Muller transform for binary-valued functions and Vilenkin-Chrestenson transform, generalized Haar, and other related transforms for multiple-valued functions
Polynomial expressions and decision diagram representations for switching and multiple-value functions
Spectral analysis of Boolean functions
Spectral synthesis and optimization of combinational and sequential devices
Spectral methods in analysis and synthesis of reliable devices
Spectral techniques for testing computer hardware
This is the authoritative reference for computer science and engineering professionals and researchers with an interest in spectral methods of representing discrete functions and related applications in the design and testing of digital devices. It is also an excellent text for graduate students in courses covering spectral logic and its applications.
Table of contents
- Cover Page
- Title Page
- Copyright
- Contents
- PREFACE
- ACKNOWLEDGEMENTS
- LIST OF FIGURES
- LIST OF TABLES
- ACRONYMS
-
CHAPTER 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
-
CHAPTER 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 DISCRETE WALSH AND VILENKIN–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
- CHAPTER 3: CALCULATION OF SPECTRAL TRANSFORMS
- CHAPTER 4: SPECTRAL METHODS IN OPTIMIZATION OF DECISION DIAGRAMS
- CHAPTER 5: ANALYSIS AND OPTIMIZATION OF LOGIC FUNCTIONS
- CHAPTER 6: SPECTRAL METHODS IN SYNTHESIS OF LOGIC NETWORKS
- CHAPTER 7: SPECTRAL METHODS OF SYNTHESIS OF SEQUENTIAL MACHINES
-
CHAPTER 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
- CHAPTER 9: SPECTRAL METHODS OF ANALYSIS AND SYNTHESIS OF RELIABLE DEVICES
-
CHAPTER 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
- CHAPTER 11: EXAMPLES OF APPLICATIONS AND GENERALIZATIONS OF SPECTRAL METHODS ON LOGIC FUNCTIONS
- APPENDIX A
- REFERENCES
- INDEX
Product information
- Title: Spectral Logic and Its Applications for the Design of Digital Devices
- Author(s):
- Release date: May 2008
- Publisher(s): Wiley-Interscience
- ISBN: 9780471731887
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