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Harmonic Analysis for Engineers and Applied Scientists

Gregory S. Chirikjian and Alexander B. Kyatkin
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
, on

This is a very wide-ranging handbook in the theory and practice of harmonic analysis (mostly Fourier, but some wavelets). It is very concise and similar in spirit to those massive tomes of engineering math, for example Kreyszig’s Advanced Engineering Mathematics. The present book is a revised Dover reprint of a 2001 CRC Press book titled Engineering Applications of Noncommutative Harmonic Analysis. Based on a little sampling and a look at the references, the revision was extensive. There is a new chapter on protein kinematics.

The book is aimed at beginning graduate students, and is intended as a supplement rather than a main textbook: it is too concise, there are no exercises, and there is far too much material even for a year-long course.There is good coverage of classical Fourier analysis on the circle and the line, but the emphasis is on harmonic analysis on groups, and much of the book applies this to particular Lie groups and motion groups of physics. A limitation is that it only covers applied math areas; there’s nothing about the many uses of Fourier analysis in pure math, so the audience is (as the title says) engineers and applied scientists.

Bottom line: an impressive work of scholarship that collects together examples from many application areas. It is well positioned for students needing a survey before they move onto more specialized work.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is His mathematical interests are number theory and classical analysis.


1. Introduction and Overview of Applications

2. Classical Fourier Analysis

3. Sturm-Liouville Expansions, Discrete Polynomial Transforms, and Wavelets

4. Orthogonal Expansions in Curvilinear Coordinates

5. Rotations in Three Dimensions

6. Rigid-Body Motion

7. Group Theory

8. Harmonic Analysis on Groups

9. Representation Theory and Operations Calculus for SU(2) and SO(3)

10. Harmonic Analysis on the Euclidean Motion Groups

11. Fast Fourier Transforms for Motion Groups

12. Robotics

13. Image Analysis and Tomography

14. Statistical Pose Determination and Camera Calibration

15. Stochastic Process, Estimation, and Control

16. Rotational Brownian Motion and Diffusion

17. Statistical Mechanics of Polymers

18. Mechanics and Texture Analysis

19. Protein Kinematics

A. Computational Complexity and Polynomials

B. Set Theory

C. Vector Spaces and Algebras

D. Matrix Functions and Decompositions

E. Techniques from Mathematical Physics

F. Variational Calculus

G. Manifolds and Riemannian Metrics