Engineering Applications Of Noncommutative Harmonic Analysis

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 555 pages
File Size : 43,8 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000697339

Get Book

Engineering Applications of Noncommutative Harmonic Analysis by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 697 pages
File Size : 54,8 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000694253

Get Book

Engineering Applications of Noncommutative Harmonic Analysis by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : Courier Dover Publications
Page : 881 pages
File Size : 52,6 Mb
Release : 2016-07-20
Category : Mathematics
ISBN : 9780486795645

Get Book

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 : Azita Mayeli
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 55,5 Mb
Release : 2013-11-08
Category : Mathematics
ISBN : 9780821894934

Get Book

Commutative and Noncommutative Harmonic Analysis and Applications by Azita Mayeli Pdf

This volume contains the proceedings of the AMS Special Session on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations, held September 22-23, 2012, at the Rochester Institute of Technology, Rochester, NY, USA. The book features new directions, results and ideas in commutative and noncommutative abstract harmonic analysis, operator theory and applications. The commutative part includes shift invariant spaces, abelian group action on Euclidean space and frame theory; the noncommutative part includes representation theory, continuous and discrete wavelets related to four dimensional Euclidean space, frames on symmetric spaces, $C DEGREES*$-algebras, projective multiresolutions, and free probability algebras. The scope of the book goes beyond traditional harmonic analysis, dealing with Fourier tools, transforms, Fourier bases, and associated function spaces. A number of papers take the step toward wavelet analysis, and even more general tools for analysis/synthesis problems, including papers on frames (over-complete bases) and their practical applications to engineering, cosmology and astrophysics.Other applications in this book include explicit families of wavelets and frames, as they are used in signal processing, multiplexing, and the study of Cosmic Microwave Background (CMB) radiation. For the purpose of organisation, the book is divided into three parts: noncommutative, commutative, and applications. The first group of papers are devoted to problems in noncommutative harmonic analysis, the second to topics in commutative harmonic analysis, and the third to such applications as wavelet and frame theory and to some real-world applications.

Author : Daniel N. Rockmore,Dennis M. Healy
Publisher : Cambridge University Press
Page : 356 pages
File Size : 45,5 Mb
Release : 2004-04-05
Category : Computers
ISBN : 052182706X

Get Book

Modern Signal Processing by Daniel N. Rockmore,Dennis M. Healy Pdf

A description of the mathematical basis of signal processing, and many areas of application.

Author : Brigitte Forster,Peter Robert Massopust
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 50,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780817648909

Get Book

Four Short Courses on Harmonic Analysis by Brigitte Forster,Peter Robert Massopust Pdf

Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.

Author : Anonim
Publisher : Unknown
Page : 410 pages
File Size : 50,5 Mb
Release : 2001
Category : Mechanics, Applied
ISBN : UIUC:30112043751830

Get Book

Applied Mechanics Reviews by Anonim Pdf

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 47,6 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

Get Book

Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : Anonim
Publisher : Unknown
Page : 1770 pages
File Size : 40,6 Mb
Release : 2004
Category : Mathematics
ISBN : UVA:X006180633

Get Book

Mathematical Reviews by Anonim Pdf

Author : Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publisher : Cambridge University Press
Page : 589 pages
File Size : 50,8 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9781107182332

Get Book

Discrete Harmonic Analysis by Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli Pdf

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

Author : Anonim
Publisher : Unknown
Page : 824 pages
File Size : 40,8 Mb
Release : 2003
Category : American literature
ISBN : UOM:39015066043145

Get Book

American Book Publishing Record by Anonim Pdf

Author : Julius S. Bendat,Allan G. Piersol
Publisher : Wiley-Interscience
Page : 486 pages
File Size : 41,5 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015029269688

Get Book

Engineering Applications of Correlation and Spectral Analysis by Julius S. Bendat,Allan G. Piersol Pdf

Expanded to cover more advanced applications where statistical properties of data can be nonstationary and the physical systems nonlinear as opposed to only linear. Stresses the practical use and interpretation of analyzed data to solve problems. Special attention is given to bias and random errors involved in desired estimates and the proper interpretation of results from specific applications. Includes numerous case studies concerned with dynamic problems which can occur in a variety of fields.

Author : Palle E. T. Jørgensen,Feng Tian (Mathematics professor)
Publisher : Unknown
Page : 533 pages
File Size : 54,9 Mb
Release : 2017
Category : Functional analysis
ISBN : 9813202130

Get Book

Non-commutative Analysis by Palle E. T. Jørgensen,Feng Tian (Mathematics professor) Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret'non-commutative analysis'broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C" algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : Mark G. Karpovsky,Radomir S. Stankovic,Jaakko T. Astola
Publisher : Wiley-Interscience
Page : 648 pages
File Size : 47,9 Mb
Release : 2008-05-27
Category : Computers
ISBN : STANFORD:36105131693082

Get Book

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 : Anonim
Publisher : Unknown
Page : 494 pages
File Size : 41,8 Mb
Release : 2004
Category : Mathematics
ISBN : UOM:39015059031891

Get Book

Bulletin of the Belgian Mathematical Society, Simon Stevin by Anonim Pdf