Fourier Analysis On Finite Groups With Applications In Signal Processing And System Design

Author : Radomir S. Stankovic,Claudio Moraga,Jaakko Astola
Publisher : John Wiley & Sons
Page : 230 pages
File Size : 43,9 Mb
Release : 2005-08-08
Category : Science
ISBN : 9780471745426

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Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design by Radomir S. Stankovic,Claudio Moraga,Jaakko Astola Pdf

Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand 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 ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : Courier Dover Publications
Page : 881 pages
File Size : 40,5 Mb
Release : 2016-07-20
Category : Mathematics
ISBN : 9780486795645

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Harmonic Analysis for Engineers and Applied Scientists by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.

Author : Robert J Marks II
Publisher : Oxford University Press
Page : 800 pages
File Size : 43,9 Mb
Release : 2009-01-08
Category : Technology & Engineering
ISBN : 0198044305

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Handbook of Fourier Analysis & Its Applications by Robert J Marks II Pdf

Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.

Author : Roberto Moreno Díaz,Franz Pichler,Alexis Quesada Arencibia
Publisher : Springer
Page : 637 pages
File Size : 46,6 Mb
Release : 2012-02-02
Category : Computers
ISBN : 9783642275791

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Computer Aided Systems Theory -- EUROCAST 2011 by Roberto Moreno Díaz,Franz Pichler,Alexis Quesada Arencibia Pdf

The two-volume proceedings, LNCS 6927 and LNCS 6928, constitute the papers presented at the 13th International Conference on Computer Aided Systems Theory, EUROCAST 2011, held in February 2011 in Las Palmas de Gran Canaria, Spain. The total of 160 papers presented were carefully reviewed and selected for inclusion in the books. The contributions are organized in topical sections on concepts and formal tools; software applications; computation and simulation in modelling biological systems; intelligent information processing; heurist problem solving; computer aided systems optimization; model-based system design, simulation, and verification; computer vision and image processing; modelling and control of mechatronic systems; biomimetic software systems; computer-based methods for clinical and academic medicine; modeling and design of complex digital systems; mobile and autonomous transportation systems; traffic behaviour, modelling and optimization; mobile computing platforms and technologies; and engineering systems applications.

Author : Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler
Publisher : Springer
Page : 360 pages
File Size : 48,6 Mb
Release : 2015-12-29
Category : Mathematics
ISBN : 9789462391635

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Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations by Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler Pdf

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.

Author : Virendra P. Sinha
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 47,7 Mb
Release : 2010-07-23
Category : Technology & Engineering
ISBN : 9789048194346

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Symmetries and Groups in Signal Processing by Virendra P. Sinha Pdf

Symmetries and Groups in Signal Processing: An Introduction deals with the subject of symmetry, and with its place and role in modern signal processing. In the sciences, symmetry considerations and related group theoretic techniques have had a place of central importance since the early twenties. In engineering, however, a matching recognition of their power is a relatively recent development. Despite that, the related literature, in the form of journal papers and research monographs, has grown enormously. A proper understanding of the concepts that have emerged in the process requires a mathematical background that goes beyond what is traditionally covered in an engineering undergraduate curriculum. Admittedly, there is a wide selection of excellent introductory textbooks on the subject of symmetry and group theory. But they are all primarily addressed to students of the sciences and mathematics, or to students of courses in mathematics. Addressed to students with an engineering background, this book is meant to help bridge the gap.

Author : Alyson Deines,Daniela Ferrero,Erica Graham,Mee Seong Im,Carrie Manore,Candice Price
Publisher : Springer
Page : 270 pages
File Size : 45,8 Mb
Release : 2018-10-31
Category : Mathematics
ISBN : 9783319986845

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Advances in the Mathematical Sciences by Alyson Deines,Daniela Ferrero,Erica Graham,Mee Seong Im,Carrie Manore,Candice Price Pdf

Featuring research from the 2017 research symposium of the Association for Women in Mathematics, this volume presents recent findings in pure mathematics and a range of advances and novel applications in fields such as engineering, biology, and medicine. Featured topics include geometric group theory, generalized iterated wreath products of cyclic groups and symmetric groups, Conway-Coxeter friezes and mutation, and classroom experiments in teaching collegiate mathematics. A review of DNA topology and a computational study of learning-induced sequence reactivation during sharp-wave ripples are also included in this volume. Numerous illustrations and tables convey key results throughout the book. This volume highlights research from women working in academia, industry, and government. It is a helpful resource for researchers and graduate students interested in an overview of the latest research in mathematics.

Author : Audrey Terras
Publisher : Cambridge University Press
Page : 456 pages
File Size : 50,7 Mb
Release : 1999-03-28
Category : Mathematics
ISBN : 0521457181

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Fourier Analysis on Finite Groups and Applications by Audrey Terras Pdf

It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.

Author : Mark G. Karpovsky,Radomir S. Stankovic,Jaakko T. Astola
Publisher : John Wiley & Sons
Page : 642 pages
File Size : 51,8 Mb
Release : 2008-07-14
Category : Computers
ISBN : 9780470289211

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Spectral Logic and Its Applications for the Design of Digital Devices by Mark G. Karpovsky,Radomir S. Stankovic,Jaakko T. Astola Pdf

Spectral techniques facilitate the design and testing of today's increasingly complex digital devices There is heightened interest in spectral techniques for the design of digital devices dictated by ever increasing demands on technology that often cannot be met by classical approaches. Spectral methods provide a uniform and consistent theoretic environment for recent achievements in this area, which appear divergent in many other approaches. Spectral Logic and Its Applications for the Design of Digital Devices gives readers a foundation for further exploration of abstract harmonic analysis over finite groups in the analysis, design, and testing of digital devices. After an introduction, this book provides the essential mathematical background for discussing spectral methods. It then delves into spectral logic and its applications, covering: * Walsh, Haar, arithmetic transform, Reed-Muller transform for binary-valued functions and Vilenkin-Chrestenson transform, generalized Haar, and other related transforms for multiple-valued functions * Polynomial expressions and decision diagram representations for switching and multiple-value functions * Spectral analysis of Boolean functions * Spectral synthesis and optimization of combinational and sequential devices * Spectral methods in analysis and synthesis of reliable devices * Spectral techniques for testing computer hardware This is the authoritative reference for computer science and engineering professionals and researchers with an interest in spectral methods of representing discrete functions and related applications in the design and testing of digital devices. It is also an excellent text for graduate students in courses covering spectral logic and its applications.

Author : Radomir S. Stanković
Publisher : Springer Nature
Page : 287 pages
File Size : 40,9 Mb
Release : 2024
Category : Electronic
ISBN : 9783031506505

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BENT FUNCTIONS AND PERMUTATION METHODS by Radomir S. Stanković Pdf

Author : Radomir S. Stankovic,Jaakko Astola,Claudio Moraga
Publisher : Springer Nature
Page : 154 pages
File Size : 41,6 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031798528

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Representations of Multiple-Valued Logic Functions by Radomir S. Stankovic,Jaakko Astola,Claudio Moraga Pdf

Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms

Author : Rolf Drechsler,Mathias Soeken
Publisher : Springer
Page : 265 pages
File Size : 47,9 Mb
Release : 2019-07-08
Category : Technology & Engineering
ISBN : 9783030203238

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Advanced Boolean Techniques by Rolf Drechsler,Mathias Soeken Pdf

This book describes recent findings in the domain of Boolean logic and Boolean algebra, covering application domains in circuit and system design, but also basic research in mathematics and theoretical computer science. Content includes invited chapters and a selection of the best papers presented at the 13th annual International Workshop on Boolean Problems. Provides a single-source reference to the state-of-the-art research in the field of logic synthesis and Boolean techniques; Includes a selection of the best papers presented at the 13th annual International Workshop on Boolean Problems; Covers Boolean algebras, Boolean logic, Boolean modeling, Combinatorial Search, Boolean and bitwise arithmetic, Software and tools for the solution of Boolean problems, Applications of Boolean logic and algebras, Applications to real-world problems, Boolean constraint solving, and Extensions of Boolean logic.

Author : Bernd Steinbach
Publisher : Cambridge Scholars Publishing
Page : 480 pages
File Size : 42,9 Mb
Release : 2016-04-26
Category : Algebra, Boolean
ISBN : 9781443892421

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Problems and New Solutions in the Boolean Domain by Bernd Steinbach Pdf

The Internet of Things is a great new challenge for the development of digital systems. In addition to the increasing number of classical unconnected digital systems, more people are regularly using new electronic devices and software that are controllable and usable by means of the internet. All such systems utilize the elementariness of Boolean values. A Boolean variable can carry only two different Boolean values: FALSE or TRUE (0 or 1), and has the best interference resistance in technical systems. However, a Boolean function exponentially depends on the number of its variables. This exponential complexity is the cause of major problems in the process of design and realization of circuits. According to Moore’s Law, the complexity of digital systems approximately doubles every 18 months. This requires comprehensive knowledge and techniques to solve complex Boolean problems. This book summarizes both new problems and solutions in the Boolean domain in solving such issues. Part 1 describes powerful new approaches in solving exceptionally complex Boolean problems. Efficient methods contribute to solving problems of extreme complexity. New algorithms and programs utilize the huge number of computing cores of the Graphical Processing Unit and improve the performance of calculations by several orders of magnitude. Part 2 represents several applications of digital systems. Due to the crucial role of the internet, both solutions and open problems regarding the security of these systems are discussed. The exploration of certain properties of such systems leads to a number of efficient solutions, which can be reused in a wide field of applications. Part 3 discusses the scientific basis of future circuit technologies, investigating the need for completely new design methods for the atomic level of quantum computers. This part also concerns itself with reversible circuits as the basis for quantum circuits and specifies important issues regarding future improvements.

Author : Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Birkhäuser
Page : 428 pages
File Size : 50,9 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319201887

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Excursions in Harmonic Analysis, Volume 4 by Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou Pdf

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Author : Roberto Moreno-Díaz,Franz Pichler,Alexis Quesada-Arencibia
Publisher : Springer
Page : 887 pages
File Size : 53,5 Mb
Release : 2015-12-17
Category : Computers
ISBN : 9783319273402

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Computer Aided Systems Theory – EUROCAST 2015 by Roberto Moreno-Díaz,Franz Pichler,Alexis Quesada-Arencibia Pdf

This volume constitutes the papers presented at the 15th International Conference on Computer Aided Systems Theory, EUROCAST 2015, held in February 2015 in Las Palmas de Gran Canaria, Spain. The total of 107 papers presented were carefully reviewed and selected for inclusion in the book. The contributions are organized in topical sections on Systems Theory and Applications; Modelling Biological Systems; Intelligent Information Processing; Theory and Applications of Metaheuristic Algorithms; Computer Methods, Virtual Reality and Image Processing for Clinical and Academic Medicine; Signals and Systems in Electronics; Model-Based System Design, Verification, and Simulation; Digital Signal Processing Methods and Applications; Modelling and Control of Robots; Mobile Platforms, Autonomous and Computing Traffic Systems; Cloud and Other Computing Systems; and Marine Sensors and Manipulators.