Spectral logic and its applications for the design of digital devices / / Mark G. Karpovsky, Radomir S. Stankovic, Jaakko T. Astola

• Record Nr.: UNINA9910877352603321
• Autore: Karpovsky Mark G
• Pubbl/distr/stampa: Hoboken, N.J., : Wiley-Interscience, c2008
• ISBN: 1-282-36540-1; 9786612365409; 0-470-28922-8; 0-470-28921-X
• Edizione: [1st edition]
• Descrizione fisica: 1 online resource (642 p.)
• Altri autori (Persone): StankovicRadomir S; AstolaJaakko
• Disciplina: 621.39/5
• Soggetti: Logic design - Methodology; Spectrum analysis; Digital electronics - Mathematics; Signal processing - Mathematics; Spectral theory (Mathematics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 554-592) and index.
• Nota di contenuto: 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 Functions2. 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 Transforms2.4.1 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; 2.7.2 Relationships to the Walsh and Vilenkin-Chrestenson Transforms, the Wiener-Khinchin Theorem; 2.7.3 Properties of Correlation Functions; 2.7.4 Generalized Autocorrelation Functions2.8 Harmonic Analysis over an Arbitrary Finite Abelian Group; 2.8.1 Definition and Properties of the Fourier Transform on Finite Abelian Groups; 2.8.2 Construction of Group Characters; 2.8.3 Fourier-Galois Transforms; 2.9 Fourier Transform on Finite Non-Abelian Groups; 2.9.1 Representation of Finite Groups; 2.9.2 Fourier Transform on Finite Non-Abelian Groups; 3. CALCULATION OF SPECTRAL TRANSFORMS; 3.1 Calculation of Walsh Spectra; 3.1.1 Matrix Interpretation of the Fast Walsh Transform; 3.1.2 Decision Diagram Methods for Calculation of Spectral Transforms3.1.3 Calculation of the Walsh Spectrum Through BDD; 3.2 Calculation of the Haar Spectrum; 3.2.1 FFT-Like Algorithms for the Haar Transform; 3.2.2 Matrix Interpretation of the Fast Haar Transform; 3.2.3 Calculation of the Haar Spectrum Through BDD; 3.3 Calculation of the Vilenkin-Chrestenson Spectrum; 3.3.1 Matrix Interpretation of the Fast Vilenkin-Chrestenson Transform; 3.3.2 Calculation of the Vilenkin-Chrestenson Transform Through Decision Diagrams; 3.4 Calculation of the Generalized Haar Spectrum; 3.5 Calculation of Autocorrelation Functions
• Sommario/riassunto: Spectral techniques facilitate the design and testingof today's increasingly complex digital devicesThere 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 harmon