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.
Autorentext
RADOMIR S. STANKOVIC, PhD, is Professor, Department of Computer 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.
Klappentext
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.
Zusammenfassung
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.
Inhalt
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 …