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.
Table of Contents
Introduction and Overview of Applications
Classical Fourier Analysis
Sturm-Liouville Expansions, Discrete Polynomial Transforms, and Wavelets
Orthogonal Expansions in Curvilinear Coordinates
Rotations in Three Dimensions
Harmonic Analysis on Groups
Representation Theory and Operational Calculus for SU(2) and SO(3)
Harmonic Analysis on the Euclidean Motion Groups
Fast Fourier Transforms for Motion Groups
Image Analysis and Tomography
Statistical Pose Determination and Camera Calibration
Stochastic Processes, Estimation, and Control
Rotational Brownian Motion and Diffusion
Statistical Mechanics of Macromolecules
Mechanics and Texture Analysis
Computational Complexity, Matrices, and Polynomials
Vector Spaces and Algebras
Techniques from Mathematical Physics
Manifolds and Riemannian Metrics
"In the opinion of this reviewer, the authors have accomplished their stated aims. [The book] is a comprehensive and generally self-contained exposition appropriate for guiding the engineering student to familiarity and, with practice, perhaps competence in an elegant and useful branch of analysis…it must certainly be considered as a solid reference addition to personal or institutional libraries. This reviewer welcomes it in his"
- Appl Mech Rev, Vol. 55, no. 1, January 2002
"There is a substantial list of over 310 references...Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups should be a source of enlightenment to the reader on many hitherto unexplored issues and concepts connecting the production and dissipation ranges of turbulence and the unstable developmental phases leading to these states. The authors have succeeded in producing a very readable and informative book that should act to stimulate additional discussions...It is recommended for research laboratory and academic library acquisition as a novel source of important developments."
-Appl Mech Rev, vol. 54, no.6, November 2001
"This book is an extensive account of the engineering applications of noncommutative harmonic analysis, that is, Fourier analysis on noncummutative Lie groups…The presentation throughout the book is explicit and highly computational. In addition, each chapter is supplemented with extensive references to the literature, both engineering and mathematical…Mathematicians will find the book interesting as a source of mathematical problems awaiting resolution, particularly those related to fast algorithms for the computation of the integrals involved"
-David H. Sattinger, Utah State University
" …comprehensible and self-contained…a valuable fuide to the literature, both engineering and mathematical. ….Although the book is intended primarily for engineers, it is also interesting for mathematicians as a source of mathematical problems."
- Mathematical Reviews, 2003g