{"product_id":"fourier-analysis-on-finite-groups-with-applications-in-signal-processing-and-system-design-9780471694632","title":"Fourier Analysis on Finite Groups with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book examines applications of Fourier analysis on finite non-Abelian groups, and discusses different methods to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as a particular example of discrete functions in engineering practice.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"…a concise monograph about the algebraic structures theory used in the Fourier analysis of signals and systems…useful for applied mathematicians and for engineers…\" (\u003ci\u003eComputing Reviews.com\u003c\/i\u003e, November 3, 2005)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003eAcronyms.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Signals and Their Mathematical Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Systems.\u003c\/p\u003e \u003cp\u003e1.2 Signals.\u003c\/p\u003e \u003cp\u003e1.3 Mathematical Models of Signals.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e2 Fourier Analysis.\u003c\/p\u003e \u003cp\u003e2.1 Representations of Groups.\u003c\/p\u003e \u003cp\u003e2.1.1 Complete Reducibility.\u003c\/p\u003e \u003cp\u003e2.2 Fourier Transform on Finite Groups.\u003c\/p\u003e \u003cp\u003e2.3 Properties of the Fourier Transform.\u003c\/p\u003e \u003cp\u003e2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003e2.5 Fast Fourier Transform on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Matrix Interpretation of the FFT.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003e3.2 Illustrative Examples.\u003c\/p\u003e \u003cp\u003e3.3 Complexity of the FFT.\u003c\/p\u003e \u003cp\u003e3.3.1 Complexity of Calculations of the FFT.\u003c\/p\u003e \u003cp\u003e3.3.2 Remarks on Programming Implememtation of FFT.\u003c\/p\u003e \u003cp\u003e3.4 FFT Through Decision Diagrams.\u003c\/p\u003e \u003cp\u003e3.4.1 Decision Diagrams.\u003c\/p\u003e \u003cp\u003e3.4.2 FFT on Finite Non-Abelian Groups Through DDs.\u003c\/p\u003e \u003cp\u003e3.4.3 MMTDs for the Fourier Spectrum.\u003c\/p\u003e \u003cp\u003e3.4.4 Complexity of DDs Calculation Methods.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e4 Optimization of Decision Diagrams.\u003c\/p\u003e \u003cp\u003e4.1 Reduction Possibilities in Decision Diagrams.\u003c\/p\u003e \u003cp\u003e4.2 Group-Theoretic Interpretation of DD.\u003c\/p\u003e \u003cp\u003e4.3 Fourier Decision Diagrams.\u003c\/p\u003e \u003cp\u003e4.3.1 Fourier Decision Trees.\u003c\/p\u003e \u003cp\u003e4.3.2 Fourier Decision Diagrams.\u003c\/p\u003e \u003cp\u003e4.4 Discussion of Different Decompositions.\u003c\/p\u003e \u003cp\u003e4.4.1 Algorithm for Optimization of DDs.\u003c\/p\u003e \u003cp\u003e4.5 Representation of Two-Variable Function Generator.\u003c\/p\u003e \u003cp\u003e4.6 Representation of Adders by Fourier DD.\u003c\/p\u003e \u003cp\u003e4.7 Representation of Multipliers by Fourier DD.\u003c\/p\u003e \u003cp\u003e4.8 Complexity of NADD.\u003c\/p\u003e \u003cp\u003e4.9 Fourier DDs with Preprocessing.\u003c\/p\u003e \u003cp\u003e4.9.1 Matrix-valued Functions.\u003c\/p\u003e \u003cp\u003e4.9.2 Fourier Transform for Matrix-Valued Functions.\u003c\/p\u003e \u003cp\u003e4.10 Fourier Decision Trees with Preprocessing.\u003c\/p\u003e \u003cp\u003e4.11 Fourier Decision Diagrams with Preprocessing.\u003c\/p\u003e \u003cp\u003e4.12 Construction of FNAPDD.\u003c\/p\u003e \u003cp\u003e4.13 Algorithm for Construction of FNAPDD.\u003c\/p\u003e \u003cp\u003e4.13.1 Algorithm for Representation.\u003c\/p\u003e \u003cp\u003e4.14 Optimization of FNAPDD.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e5 Functional Expressions on Quaternion Groups.\u003c\/p\u003e \u003cp\u003e5.1 Fourier Expressions on Finite Dyadic Groups.\u003c\/p\u003e \u003cp\u003e5.1.1 Finite Dyadic Groups.\u003c\/p\u003e \u003cp\u003e5.2 Fourier Expressions on Q\u003csub\u003e2\u003c\/sub\u003e.\u003c\/p\u003e \u003cp\u003e5.3 Arithmetic Expressions.\u003c\/p\u003e \u003cp\u003e5.4 Arithmetic Expressions from Walsh Expansions.\u003c\/p\u003e \u003cp\u003e5.5 Arithmetic Expressions on Q\u003csub\u003e2\u003c\/sub\u003e.\u003c\/p\u003e \u003cp\u003e5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions.\u003c\/p\u003e \u003cp\u003e5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions.\u003c\/p\u003e \u003cp\u003e5.6 Different Polarity Polynomials Expressions.\u003c\/p\u003e \u003cp\u003e5.6.1 Fixed-Polarity Fourier Expressions in C(Q\u003csub\u003e2\u003c\/sub\u003e).\u003c\/p\u003e \u003cp\u003e5.6.2 Fixed-Polarity Arithmetic-Haar Expressions.\u003c\/p\u003e \u003cp\u003e5.7 Calculation of the Arithmetic-Haar Coefficients.\u003c\/p\u003e \u003cp\u003e5.7.1 FFT-like Algorithm.\u003c\/p\u003e \u003cp\u003e5.7.2 Calculation of Arithmetic-Haar Coefficients Through Decision Diagrams.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Gibbs Derivatives on Finite Groups.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Definition and Properties of Gibbs Derivatives on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003e6.2 Gibbs Anti-Derivative.\u003c\/p\u003e \u003cp\u003e6.3 Partial Gibbs Derivatives.\u003c\/p\u003e \u003cp\u003e6.4 Gibbs Differential Equations.\u003c\/p\u003e \u003cp\u003e6.5 Matrix Interpretation of Gibbs Derivatives.\u003c\/p\u003e \u003cp\u003e6.6 Fast Algorithms for Calculation of Gibbs Derivatives on Finite Groups.\u003c\/p\u003e \u003cp\u003e6.6.1 Complexity of Calculation of Gibbs Derivatives.\u003c\/p\u003e \u003cp\u003e6.7 Calculation of Gibbs Derivatives Through DDs.\u003c\/p\u003e \u003cp\u003e6.7.1 Calculation of Partial Gibbs Derivatives. \u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Linear Systems on Finite Non-Abelian Groups.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Linear Shift-Invariant Systems on Groups.\u003c\/p\u003e \u003cp\u003e7.2 Linear Shift-Invariant Systems on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003e7.3 Gibbs Derivatives and Linear Systems.\u003c\/p\u003e \u003cp\u003e7.3.1 Discussion.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Hilbert Transform on Finite Groups.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Some Results of Fourier Analysis on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003e8.2 Hilbert Transform on Finite Non-Abelian Groups.\u003c\/p\u003e \u003cp\u003e8.3 Hilbert Transform in Finite Fields.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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