Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design (PDF)
(Sprache: Englisch)
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...
groups
The majority of publications in spectral techniques consider
Fourier transform on Abelian groups. However, non-Abelian groups
provide notable advantages in efficient...
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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.
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.
Inhaltsverzeichnis zu „Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design (PDF)“
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.
... mehr
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.
... weniger
Autoren-Porträt von Radomir S. Stankovic, Claudio Moraga, Jaakko Astola
RADOMIR S. STANKOVIC, PhD, is Professor, Department ofComputer Science, Faculty of Electronics, University of Nis,
Serbia.
CLAUDIO MORAGA, PhD, is Professor, Department of Computer
Science, Dortmund University, Germany.
JAAKKO T. ASTOLA, PhD, is Professor, Institute of Signal
Processing, Tampere University of Technology, Finland.
Bibliographische Angaben
- Autoren: Radomir S. Stankovic , Claudio Moraga , Jaakko Astola
- 2005, 1. Auflage, 230 Seiten, Englisch
- Verlag: John Wiley & Sons
- ISBN-10: 0471745421
- ISBN-13: 9780471745426
- Erscheinungsdatum: 25.07.2005
Abhängig von Bildschirmgrösse und eingestellter Schriftgrösse kann die Seitenzahl auf Ihrem Lesegerät variieren.
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