A Student's Guide to Fourier Transforms

A Student's Guide to Fourier Transforms : With Applications in Physics and Engineering

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Fourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through 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 Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert-Zernike theorem, Babinet's principle and dipole arrays.show more

Product details

  • Electronic book text | 160 pages
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • Revised
  • 3rd Revised edition
  • 73 b/w illus.
  • 1139065777
  • 9781139065771

About J. F. James

John James has held teaching positions at the University of Minnesota, Queen's University, Belfast and the University of Manchester. He is a Fellow of the Royal Astronomical Society, a member of the Optical Society of America and of the International Astronomical Union. His research interests include the invention, design and construction of astronomical instruments and their use in astronomy, cosmology and upper-atmosphere physics.show more

Review quote

From previous editions: '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 Analysisshow more

Table of contents

1. Physics and Fourier transforms; 2. Useful properties and theorems; 3. Applications 1: Fraunhofer diffraction; 4. Applications 2: signal analysis and communication theory; 5. Applications 3: 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 transforms; 10. Appendix; 11. Bibliography; 12. Index.show more