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.
Autorentext
Mark G. Karpovsky, PhD, is Professor of Computer Engineering at the College of Engineering and Director of Reliable Computing Laboratory, both at Boston University. Dr. Karpovsky authored the classic reference Finite Orthogonal Series in the Design of Digital Devices (Wiley). He has published more than 150 research papers and several books on the design of reliable computer and communications networks.
Radomir S. Stankovic is Professor of Computer Logic Design at the Department of Computer Science at University of Ni, Serbia. He has been a visiting researcher/faculty member at Kyushu Institute of Technology, Japan, and Tampere University of Technology, Finland.
Jaakko T. Astola has held academic positions in mathematics, applied mathematics, and computer science. Since 1993, he has been Professor of Signal Processing at Tampere University, Finland, and Director of Tampere International Center for Signal Processing. He has published over 150 research papers and several books on signal processing.
Klappentext
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.
Zusammenfassung
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.
Inhalt
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 ReedMuller 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 andVilenkinChrestenson Transforms.
2.7 Autocorrelation and Cross-Correlation Functions.
2.8 Harmonic Analysis over an Arbitrary Finite Abelian Group.
2.9 Fourier Transform on Finite NonAbelian Groups.
3. CALCULATION OF SPECTRAL TRANSFORMS.<…