LEADER 05727nam 2200745 a 450 001 9910877352603321 005 20200520144314.0 010 $a1-282-36540-1 010 $a9786612365409 010 $a0-470-28922-8 010 $a0-470-28921-X 035 $a(CKB)1000000000687467 035 $a(EBL)468585 035 $a(SSID)ssj0000310065 035 $a(PQKBManifestationID)11229893 035 $a(PQKBTitleCode)TC0000310065 035 $a(PQKBWorkID)10303124 035 $a(PQKB)11279410 035 $a(MiAaPQ)EBC468585 035 $a(CaSebORM)9780471731887 035 $a(OCoLC)232612145 035 $a(OCoLC)840106058 035 $a(OCoLC)ocn840106058 035 $a(EXLCZ)991000000000687467 100 $a20080118d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral logic and its applications for the design of digital devices /$fMark G. Karpovsky, Radomir S. Stankovic, Jaakko T. Astola 205 $a1st edition 210 $aHoboken, N.J. $cWiley-Interscience$dc2008 215 $a1 online resource (642 p.) 300 $aDescription based upon print version of record. 311 $a0-471-73188-9 320 $aIncludes bibliographical references (p. 554-592) and index. 327 $aSPECTRAL 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 327 $a1.8 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 327 $a2.4 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 327 $a2.7.4 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 327 $a3.1.2 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 327 $a3.5 Calculation of Autocorrelation Functions 330 $aSpectral 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 606 $aLogic design$xMethodology 606 $aSpectrum analysis 606 $aDigital electronics$xMathematics 606 $aSignal processing$xMathematics 606 $aSpectral theory (Mathematics) 615 0$aLogic design$xMethodology. 615 0$aSpectrum analysis. 615 0$aDigital electronics$xMathematics. 615 0$aSignal processing$xMathematics. 615 0$aSpectral theory (Mathematics) 676 $a621.39/5 700 $aKarpovsky$b Mark G$01762626 701 $aStankovic$b Radomir S$01731465 701 $aAstola$b Jaakko$01750436 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877352603321 996 $aSpectral logic and its applications for the design of digital devices$94202660 997 $aUNINA