000 08972nam a2201045 i 4500
001 5237943
003 IEEE
005 20220712205619.0
006 m o d
007 cr |n|||||||||
008 151221s2005 njua ob 001 eng d
020 _a1601193769
_qlivre �aelectronique
020 _a9780471745433
_qelectronic
020 _a9781601193766
020 _z0471694630
_qpaper
020 _z9780471694632
_qprint
020 _z047174543X
_qelectronic
020 _z9780471745426
_qelectronic
020 _z0471745421
_qelectronic
024 7 _a10.1002/047174543X
_2doi
035 _a(CaBNVSL)mat05237943
035 _a(IDAMS)0b00006481095e37
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aTK5102.9
_b.S696 2005eb
082 0 4 _a621.382/2
_222
100 1 _aStankovi�ac, Radomir S.,
_eauthor.
_926504
245 1 0 _aFourier analysis on finite groups with applications in signal processing and system design /
_cRadomir S. Stankovi�ac, Claudio Moraga, Jaakko Astola.
264 1 _aPiscataway, New Jersey :
_bIEEE Press,
_cc2005.
264 2 _a[Piscataqay, New Jersey] :
_bIEEE Xplore,
_c[2005]
300 _a1 PDF (xxiii, 236 pages) :
_billustrations.
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
504 _aIncludes bibliographical references.
505 0 _aPreface -- Acknowledgments -- Acronyms -- 1 Signals and Their Mathematical Models -- 1.1 Systems -- 1.2 Signals -- 1.3 Mathematical Models of Signals -- References -- 2 Fourier Analysis -- 2.1 Representations of Groups -- 2.1.1 Complete Reducibility -- 2.2 Fourier Transform on Finite Groups -- 2.3 Properties of the Fourier Transform -- 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups -- 2.5 Fast Fourier Transform on Finite Non-Abelian Groups -- References -- 3 Matrix Interpretation of the FFT -- 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups -- 3.2 Illustrative Examples -- 3.3 Complexity of the FFT -- 3.3.1 Complexity of Calculations of the FFT -- 3.3.2 Remarks on Programming Implememtation of FFT -- 3.4 FFT Through Decision Diagrams -- 3.4.1 Decision Diagrams -- 3.4.2 FFT on Finite Non-Abelian Groups Through DDs -- 3.4.3 MMTDs for the Fourier Spectrum -- 3.4.4 Complexity of DDs Calculation Methods -- References -- 4 Optimization of Decision Diagrams -- 4.1 Reduction Possibilities in Decision Diagrams -- 4.2 Group-Theoretic Interpretation of DD -- 4.3 Fourier Decision Diagrams -- 4.3.1 Fourier Decision Trees -- 4.3.2 Fourier Decision Diagrams -- 4.4 Discussion of Different Decompositions -- 4.4.1 Algorithm for Optimization of DDs -- 4.5 Representation of Two-Variable Function Generator -- 4.6 Representation of Adders by Fourier DD -- 4.7 Representation of Multipliers by Fourier DD -- 4.8 Complexity of NADD -- 4.9 Fourier DDs with Preprocessing -- 4.9.1 Matrix-valued Functions -- 4.9.2 Fourier Transform for Matrix-Valued Functions -- 4.10 Fourier Decision Trees with Preprocessing -- 4.11 Fourier Decision Diagrams with Preprocessing -- 4.12 Construction of FNAPDD -- 4.13 Algorithm for Construction of FNAPDD -- 4.13.1 Algorithm for Representation -- 4.14 Optimization of FNAPDD -- References -- 5 Functional Expressions on Quaternion Groups -- 5.1 Fourier Expressions on Finite Dyadic Groups -- 5.1.1 Finite Dyadic Groups -- 5.2 Fourier Expressions on Q2.
505 8 _a5.3 Arithmetic Expressions -- 5.4 Arithmetic Expressions from Walsh Expansions -- 5.5 Arithmetic Expressions on Q2 -- 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions -- 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions -- 5.6 Different Polarity Polynomials Expressions -- 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2) -- 5.6.2 Fixed-Polarity Arithmetic-Haar�Expressions -- 5.7 Calculation of the Arithmetic-Haar Coefficients -- 5.7.1 FFT-like Algorithm -- 5.7.2 Calculation of Arithmetic-Haar Coefficients Through Decision Diagrams -- References -- 6 Gibbs Derivatives on Finite Groups -- 6.1 Definition and Properties of Gibbs Derivatives on Finite Non-Abelian Groups -- 6.2 Gibbs Anti-Derivative -- 6.3 Partial Gibbs Derivatives -- 6.4 Gibbs Differential Equations -- 6.5 Matrix Interpretation of Gibbs Derivatives -- 6.6 Fast Algorithms for Calculation of Gibbs Derivatives on Finite Groups -- 6.6.1 Complexity of Calculation of Gibbs Derivatives -- 6.7 Calculation of Gibbs Derivatives Through DDs -- 6.7.1 Calculation of Partial Gibbs Derivatives.� -- References -- 7 Linear Systems on Finite Non-Abelian Groups -- 7.1 Linear Shift-Invariant Systems on Groups -- 7.2 Linear Shift-Invariant Systems on Finite Non-Abelian Groups -- 7.3 Gibbs Derivatives and Linear Systems -- 7.3.1 Discussion -- References -- 8 Hilbert Transform on Finite Groups -- 8.1 Some Results of Fourier Analysis on Finite Non-Abelian Groups -- 8.2 Hilbert Transform on Finite Non-Abelian Groups -- 8.3 Hilbert Transform in Finite Fields -- References -- Index.
506 1 _aRestricted to subscribers or individual electronic text purchasers.
520 _aDiscover applications of Fourier analysis on finite non-Abelian groups The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods. Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design examines aspects of Fourier analysis on finite non-Abelian groups and discusses different methods used to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as an example of discrete functions in engineering practice. Additionally, consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelian groups. A solid foundation of this complex topic is provided by beginning with a review of signals and their mathematical models and Fourier analysis. Next, the book examines recent achievements and discoveries in: . Matrix interpretation of the fast Fourier transform. Optimization of decision diagrams. Functional expressions on quaternion groups. Gibbs derivatives on finite groups. Linear systems on finite non-Abelian groups. Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups in compact representations of discrete functions and related tasks in signal processing and system design, including logic design. All chapters are self-contained, each with a list of references to facilitate the development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this is an excellent textbook for graduate-level students and researchers in signal processing, logic design, and system theory-as well as the more general topics of computer science and applied mathematics.
530 _aAlso available in print.
538 _aMode of access: World Wide Web
588 _aDescription based on PDF viewed 12/21/2015.
650 0 _aSignal processing
_xMathematics.
_93827
650 0 _aFourier analysis.
_96642
650 0 _aNon-Abelian groups.
_926505
655 0 _aElectronic books.
_93294
695 _aApproximation methods
695 _aBooks
695 _aBoolean functions
695 _aChannel coding
695 _aComputational modeling
695 _aConvolution
695 _aData structures
695 _aDecision trees
695 _aDifferential equations
695 _aDigital filters
695 _aDiscrete Fourier transforms
695 _aEigenvalues and eigenfunctions
695 _aError probability
695 _aFast Fourier transforms
695 _aFiltering
695 _aFinite element methods
695 _aFourier transforms
695 _aGalois fields
695 _aGraphics
695 _aHarmonic analysis
695 _aIndexes
695 _aIntegrated circuits
695 _aKernel
695 _aLinear systems
695 _aLinearity
695 _aMathematical model
695 _aOptimization
695 _aPolynomials
695 _aQuaternions
695 _aSignal processing
695 _aSignal processing algorithms
695 _aSparse matrices
695 _aSwitches
695 _aSymmetric matrices
695 _aTopology
695 _aVectors
700 1 _aMoraga, Claudio.
_926506
700 1 _aAstola, Jaakko T.
_926507
710 2 _aIEEE Xplore (Online Service),
_edistributor.
_926508
710 2 _aJohn Wiley & Sons,
_epublisher.
_96902
730 0 _aKnovel
_h[ressource �aelectronique].
_926509
776 0 8 _iPrint version:
_z9780471694632
856 4 2 _3Abstract with links to resource
_uhttps://ieeexplore.ieee.org/xpl/bkabstractplus.jsp?bkn=5237943
942 _cEBK
999 _c73795
_d73795