Spectral Logic and Its Applications for the Design of Digital Devices

Abstract

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.