A Student's Guide to Fourier Transforms : With Applications in Physics and Engineering
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.
- Electronic book text
- 05 Jun 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 2nd Revised edition
- 76 b/w illus.
From reviews of the first edition: '... elegantly simple.' New Scientist 'It is the wide range of topics that makes this book so appealing ... I highly recommend this book for the advanced student ... Even the expert who wants a deeper appreciation of the Fourier transform will find the book useful.' Computers in Physics '... this is an excellent book to initiate students who possess a reasonable mathematical background to the use of Fourier transforms ...' Microscopy and Analysis
Table of contents
Preface to the first edition; Preface to the second edition; 1. Physics and Fourier transforms; 2. Useful properties and theorems; 3. Applications I: Fraunhofer diffraction; 4. Applications II: signal analysis and communication theory; 5. Applications III: spectroscopy and spectral line shapes; 6. Two-dimensional Fourier transforms; 7. Multi-dimensional Fourier transforms; 8. The formal complex Fourier transform; 9. Discrete and digital Fourier transform; Appendix; Bibliography.