Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola

• Record Nr.: UNISA996212283503316
• Autore: Stankoviâc Radomir S.
• Pubbl/distr/stampa: Piscataway, New Jersey : , : IEEE Press, , c2005; [Piscataqay, New Jersey] : , : IEEE Xplore, , [2005]
• ISBN: 1-280-27793-9; 9786610277933; 0-471-74543-X; 1-60119-376-9; 0-471-74542-1
• Descrizione fisica: 1 online resource (262 p.)
• Altri autori (Persone): MoragaClaudio; AstolaJaakko T
• Disciplina: 621.3822; 621.38220151
• Soggetti: Signal processing - Mathematics; Fourier analysis; Non-Abelian groups
• 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 and index.
• Nota di contenuto: Preface -- 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.; 5.3 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<U+0083>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.<U+0083> -- 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.
• Sommario/riassunto: Discover 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.

Engaged language policy and practices / / Kathryn A. Davis, Prem Phyak

• Record Nr.: UNINA9910155127703321
• Autore: Davis Kathryn Anne
• Pubbl/distr/stampa: London : , : Routledge, , 2016
• ISBN: 1-317-44248-2; 1-315-69528-6; 1-317-44249-0; 9781315695280
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (147 pages)
• Disciplina: 306.44/9; 306.449
• Soggetti: Language policy - Political aspects; Language planning - Political aspects; Language and languages - Political aspects; Intercultural communication; Language and culture; Sociolinguistics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Introduction -- Language policies and ideological analyses -- Engaged ethnography as transformative -- Language policy processes -- Planning resistance and discovering alternatives -- Developing relevant and engaging language policies and practices -- Afterword: Language policy rights and resources.
• Sommario/riassunto: Engaged Language Policy and Practices re-envisions language policy and planning as an engaged approach, drawing on and portraying theoretical and educational equity perspectives. It calls for the right to language policy-making in which all concerned--communities, parents, students, educators, and advocates--collectively imagine new strategies for resisting global neoliberal marginalization of home languages and cultural identities. This book subsequently emphasizes the means by which engaged dialectic processes can inform and clarify language policy-making decisions that promote equity. In other words, rather than descriptions of outcomes, the authors emphasize the need to detail the means by which local/regional actors resist and transform inequitable policies. These descriptions of processes thereby provide all actors with ideological, pedagogical, and equity policy tools that can inform situated school and community policy-making. This book depicts ways in which engaged language policy embodies the intersection of critical inquiry, participant involvement, and ongoing engaged language planning processes. It further offers an alternative to the traditional top-down approach to language education policy-making. Engaged Language Policy and Practices is essential reading for scholars, teachers, students, communities, and others concerned with worldwide language and identity equity.