Fourier analysis on finite groups with applications in signal processing and system design / (Record no. 40058)
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| fixed length control field | 08886nam a2201033 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 5237943 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20230927112344.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr |n||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 151221s2005 njua ob 001 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1601193769 |
| Qualifying information | livre �aelectronique |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780471745433 |
| Qualifying information | electronic |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781601193766 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0471694630 |
| Qualifying information | paper |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780471694632 |
| Qualifying information | |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 047174543X |
| Qualifying information | electronic |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780471745426 |
| Qualifying information | electronic |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0471745421 |
| Qualifying information | electronic |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1002/047174543X |
| Source of number or code | doi |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaBNVSL)mat05237943 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (IDAMS)0b00006481095e37 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | CaBNVSL |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | CaBNVSL |
| Modifying agency | CaBNVSL |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 621.382/2 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Stankovi�ac, Radomir S., |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Fourier analysis on finite groups with applications in signal processing and system design / |
| Statement of responsibility, etc. | Radomir S. Stankovi�ac, Claudio Moraga, Jaakko Astola. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Piscataway, New Jersey : |
| Name of producer, publisher, distributor, manufacturer | IEEE Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | c2005. |
| 264 #2 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | [Piscataqay, New Jersey] : |
| Name of producer, publisher, distributor, manufacturer | IEEE Xplore, |
| Date of production, publication, distribution, manufacture, or copyright notice | [2005] |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 PDF (xxiii, 236 pages) : |
| Other physical details | illustrations. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | electronic |
| Source | isbdmedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Source | rdacarrier |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Includes bibliographical references. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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�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# - RESTRICTIONS ON ACCESS NOTE | |
| Terms governing access | Restricted to subscribers or individual electronic text purchasers. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE | |
| Additional physical form available note | Also available in print. |
| 538 ## - SYSTEM DETAILS NOTE | |
| System details note | Mode of access: World Wide Web |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on PDF viewed 12/21/2015. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Signal processing |
| General subdivision | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Fourier analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Non-Abelian groups. |
| 655 #0 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 695 ## - | |
| -- | Approximation methods |
| 695 ## - | |
| -- | Books |
| 695 ## - | |
| -- | Boolean functions |
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| -- | Channel coding |
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| -- | Computational modeling |
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| -- | Convolution |
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| -- | Data structures |
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| -- | Decision trees |
| 695 ## - | |
| -- | Differential equations |
| 695 ## - | |
| -- | Digital filters |
| 695 ## - | |
| -- | Discrete Fourier transforms |
| 695 ## - | |
| -- | Eigenvalues and eigenfunctions |
| 695 ## - | |
| -- | Error probability |
| 695 ## - | |
| -- | Fast Fourier transforms |
| 695 ## - | |
| -- | Filtering |
| 695 ## - | |
| -- | Finite element methods |
| 695 ## - | |
| -- | Fourier transforms |
| 695 ## - | |
| -- | Galois fields |
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| -- | Graphics |
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| -- | Harmonic analysis |
| 695 ## - | |
| -- | Indexes |
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| -- | Integrated circuits |
| 695 ## - | |
| -- | Kernel |
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| -- | Linear systems |
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| -- | Linearity |
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| -- | Mathematical model |
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| -- | Optimization |
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| -- | Polynomials |
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| -- | Quaternions |
| 695 ## - | |
| -- | Signal processing |
| 695 ## - | |
| -- | Signal processing algorithms |
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| -- | Sparse matrices |
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| -- | Switches |
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| -- | Symmetric matrices |
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| -- | Topology |
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| -- | Vectors |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Moraga, Claudio. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Astola, Jaakko T. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | IEEE Xplore (Online Service), |
| Relator term | distributor. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | John Wiley & Sons, |
| Relator term | publisher. |
| 730 0# - ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Knovel |
| Medium | [ressource �aelectronique]. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| International Standard Book Number | 9780471694632 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | Abstract with links to resource |
| Uniform Resource Identifier | <a href="https://ieeexplore.ieee.org/xpl/bkabstractplus.jsp?bkn=5237943">https://ieeexplore.ieee.org/xpl/bkabstractplus.jsp?bkn=5237943</a> |
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