Spectral Logic and Its Applications for the Design of Digital Devices

CONTENTS

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

1.4.1 Decision Trees

1.4.2 Decision Diagrams

1.4.3 Decision Diagrams for Multiple-Valued 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

2.3.1 Basis Functions

2.3.2 Walsh Functions

2.3.2.1 Ordering of Walsh Functions

2.3.2.2 Properties of Walsh Functions

2.3.2.3 Hardware Implementations of Walsh Functions

2.3.3 Haar Functions

2.3.3.1 Ordering of Haar Functions

2.3.3.2 Properties of Haar Functions

2.3.3.3 Hardware Implementation of Haar Functions

2.3.3.4 Hardware Implementation of the Inverse Haar Transform

2.4 Walsh Related Transforms

2.4.1 Arithmetic Transform

2.4.2 Arithmetic Expressions from Walsh Expansions

2.5 Bases for Systems of Multiple-Valued Functions

2.5.1 Vilenkin–Chrestenson Functions and Their Properties

2.5.2 Generalized Haar Functions

2.6 Properties of Discrete Walsh and Vilenkin–Chrestenson Transforms

2.7 Autocorrelation and Cross-Correlation Functions

2.7.1 Definitions of Autocorrelation and Cross-Correlation Functions ...