Symmetries And Groups In Signal Processing

Author : Virendra P. Sinha
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 41,8 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 : Ahmed G. Radwan,Farooq Ahmad Khanday,Lobna A. Said
Publisher : Academic Press
Page : 530 pages
File Size : 40,9 Mb
Release : 2021-10-22
Category : Technology & Engineering
ISBN : 9780323902038

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Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control by Ahmed G. Radwan,Farooq Ahmad Khanday,Lobna A. Said Pdf

Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. Presents a simple and comprehensive understanding of the field of fractional-order systems Offers practical knowledge on the design of fractional-order systems for different applications Exposes users to possible new applications for fractional-order systems

Author : Max A. Little
Publisher : Oxford University Press, USA
Page : 378 pages
File Size : 43,9 Mb
Release : 2019
Category : Computers
ISBN : 9780198714934

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Machine Learning for Signal Processing by Max A. Little Pdf

Describes in detail the fundamental mathematics and algorithms of machine learning (an example of artificial intelligence) and signal processing, two of the most important and exciting technologies in the modern information economy. Builds up concepts gradually so that the ideas and algorithms can be implemented in practical software applications.

Author : Andrey Popoff
Publisher : CRC Press
Page : 449 pages
File Size : 55,6 Mb
Release : 2022-04-19
Category : Technology & Engineering
ISBN : 9781000571974

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Fundamentals of Signal Processing in Generalized Metric Spaces by Andrey Popoff Pdf

Exploring the interrelations between generalized metric spaces, lattice-ordered groups, and order statistics, the book contains a new algebraic approach to Signal Processing Theory. It describes mathematical concepts and results important in the development, analysis, and optimization of signal processing algorithms intended for various applications. The book offers a solution of large-scale Signal Processing Theory problems of increasing both signal processing efficiency under prior uncertainty conditions and signal processing rate that is provided by multiplication-free signal processing algorithms based on lattice-ordered group operations. From simple basic relationships to computer simulation, the text covers a wide range of new mathematical techniques essential for understanding the proposed signal processing algorithms developed for solving the following problems: signal parameter and spectral estimation, signal filtering, detection, classification, and resolution; array signal processing; demultiplexing and demodulation in multi-channel communication systems and multi-station networks; wavelet analysis of 1D/ 2D signals. Along with discussing mathematical aspects, each chapter presents examples illustrating operation of signal processing algorithms developed for various applications. The book helps readers understand relations between known classic and obtained results as well as recent research trends in Signal Processing Theory and its applications, providing all necessary mathematical background concerning lattice-ordered groups to prepare readers for independent work in the marked directions including more advanced research and development.

Author : Bernard L. Johnston
Publisher : CRC Press
Page : 276 pages
File Size : 42,7 Mb
Release : 2020-07-25
Category : Mathematics
ISBN : 9781000153378

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Numbers and Symmetry by Bernard L. Johnston Pdf

This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism. Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures. In terms of classical algebraic structures, the text divides roughly into three parts:

Author : Chengming Bai
Publisher : World Scientific
Page : 665 pages
File Size : 40,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814518550

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Symmetries and Groups in Contemporary Physics by Chengming Bai Pdf

This volume focuses on developments in the field of group theory in its broadest sense and is of interest to theoretical and experimental physicists, mathematicians, and scientists in related disciplines who are interested in the latest methods and applications. In an increasingly ultra-specialized world, this volume will demonstrate the interchange of ideas and methods in theoretical and mathematical physics.

Author : Eric Dubois
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 54,5 Mb
Release : 2019-03-12
Category : Technology & Engineering
ISBN : 9781119111757

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Multidimensional Signal and Color Image Processing Using Lattices by Eric Dubois Pdf

An Innovative Approach to Multidimensional Signals and Systems Theory for Image and Video Processing In this volume, Eric Dubois further develops the theory of multi-D signal processing wherein input and output are vector-value signals. With this framework, he introduces the reader to crucial concepts in signal processing such as continuous- and discrete-domain signals and systems, discrete-domain periodic signals, sampling and reconstruction, light and color, random field models, image representation and more. While most treatments use normalized representations for non-rectangular sampling, this approach obscures much of the geometrical and scale information of the signal. In contrast, Dr. Dubois uses actual units of space-time and frequency. Basis-independent representations appear as much as possible, and the basis is introduced where needed to perform calculations or implementations. Thus, lattice theory is developed from the beginning and rectangular sampling is treated as a special case. This is especially significant in the treatment of color and color image processing and for discrete transform representations based on symmetry groups, including fast computational algorithms. Other features include: An entire chapter on lattices, giving the reader a thorough grounding in the use of lattices in signal processing Extensive treatment of lattices as used to describe discrete-domain signals and signal periodicities Chapters on sampling and reconstruction, random field models, symmetry invariant signals and systems and multidimensional Fourier transformation properties Supplemented throughout with MATLAB examples and accompanying downloadable source code Graduate and doctoral students as well as senior undergraduates and professionals working in signal processing or video/image processing and imaging will appreciate this fresh approach to multidimensional signals and systems theory, both as a thorough introduction to the subject and as inspiration for future research.

Author : Rubakov Valery A,Isaev Alexey P
Publisher : World Scientific
Page : 476 pages
File Size : 43,6 Mb
Release : 2018-03-21
Category : Science
ISBN : 9789813236875

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Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras by Rubakov Valery A,Isaev Alexey P Pdf

The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence. The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics. Contents: Preface Groups and Transformations Lie Groups Lie Algebras Representations of Groups and Lie Algebras Compact Lie Algebras Root Systems and Classification of Simple Lie Algebras Homogeneous Spaces and their Geometry Solutions to Selected Problems Selected Bibliography References Index Readership: Graduate students and researchers in theoretical physics and mathematical physics. Keywords: Lie Groups;Lie Algebras;Representation Theory;Conformal Symmetries;Yangians;Coset Spaces;Differential Geometry;Casimir Operators;Root Systems;AdS Spaces;Lobachevskian GeometryReview:0

Author : Serge Dos Santos,Mostafa Maslouhi,Kasso A. Okoudjou
Publisher : Springer Nature
Page : 190 pages
File Size : 47,6 Mb
Release : 2020-02-21
Category : Mathematics
ISBN : 9783030352028

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Recent Advances in Mathematics and Technology by Serge Dos Santos,Mostafa Maslouhi,Kasso A. Okoudjou Pdf

The chapters in this volume are based on talks given at the inaugural Technology, Engineering and Mathematics Conference (TEM18), held from March 26 to 27, 2018 in Kenitra, Morocco. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields. There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Topics include: Harmonic analysis Big data analytics and applications Biomathematics Computer engineering and applications Economics and financial engineering Medical imaging and non-destructive testing This volume is ideal for engineers and researchers working in technological fields that need to be modeled and simulated using the tools of modern mathematics.

Author : Hongjiang Song
Publisher : Lulu.com
Page : 316 pages
File Size : 52,7 Mb
Release : 2014-03-21
Category : Technology & Engineering
ISBN : 9781312051300

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The Arts of VLSI Opamp Circuit Design - A Structural Approach Based on Symmetry by Hongjiang Song Pdf

This text is developed from the notes of a VLSI circuit design class (EEE598) the author offered in Engineering School at Arizona State University. The materials cover the structural design approaches of VLSI operational amplifier circuits based on the symmetry principle, symmetry circuit structures, prototype circuits, and symmetry scaling/transformation techniques.

Author : Nigel Boston
Publisher : Springer Science & Business Media
Page : 56 pages
File Size : 54,8 Mb
Release : 2012-04-23
Category : Technology & Engineering
ISBN : 9781461438632

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Applications of Algebra to Communications, Control, and Signal Processing by Nigel Boston Pdf

Over the last 50 years there have been an increasing number of applications of algebraic tools to solve problems in communications, in particular in the fields of error-control codes and cryptography. More recently, broader applications have emerged, requiring quite sophisticated algebra - for example, the Alamouti scheme in MIMO communications is just Hamilton's quaternions in disguise and has spawned the use of PhD-level algebra to produce generalizations. Likewise, in the absence of credible alternatives, the industry has in many cases been forced to adopt elliptic curve cryptography. In addition, algebra has been successfully applied to problems in signal processing such as face recognition, biometrics, control design, and signal design for radar. This book introduces the reader to the algebra they need to appreciate these developments and to various problems solved by these techniques.

Author : Hamid Krim,A. Ben Hamza
Publisher : Cambridge University Press
Page : 299 pages
File Size : 46,5 Mb
Release : 2015-06-18
Category : Computers
ISBN : 9781107033900

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Geometric Methods in Signal and Image Analysis by Hamid Krim,A. Ben Hamza Pdf

A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.

Author : N.B. Singh
Publisher : N.B. Singh
Page : 130 pages
File Size : 50,6 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Abstract Algebra: Group Theory by N.B. Singh Pdf

Author : Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan
Publisher : Springer
Page : 406 pages
File Size : 50,5 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9783319498874

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Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications by Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan Pdf

Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.

Author : Marlos A.G. Viana,Vasudevan Lakshminarayanan
Publisher : CRC Press
Page : 134 pages
File Size : 44,9 Mb
Release : 2019-11-27
Category : Technology & Engineering
ISBN : 9780429528163

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Symmetry in Optics and Vision Studies by Marlos A.G. Viana,Vasudevan Lakshminarayanan Pdf

This book presents an introduction to the foundations, interpretations, and data-analytic applications of symmetry studies with an emphasis on applications in optical sciences. Symmetry studies connect group theoretic and statistical methods for data summary and inference. Readers should have an understanding of calculus and linear algebra as well as introductory statistics. The book reviews finite group theory in the introductory chapters. Computational tools used in the text are available for download in the form of Mathmaticaâ notebooks or R scripts. This book: Demonstrates the usefulness of a unified view of algebra and symmetry studies to address data-analytic questions in optics and vision science Offers a brief review of finite group theory and elements of multivariate analysis Includes various examples from diverse areas of optical science