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. 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...
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.
Table of contents:
1. Physics and Fourier transforms; 2. Useful properties and theorems; 3. Applications I: Fraunhofer diffraction; 4. Applications II: communication theory; 5. Applications III: spectroscopy; 6. Two-dimensional transforms; 7. Multi-dimensional transforms; 8. The formal complex Fourier transform; 9. Discrete and digital Fourier transforms; Appendix: mathematical proofs.
A new edition of a successful textbook for students in physics, computer science and electrical engineering. Important ideas in practical science and information technology are described at an understandable level. The book covers the field broadly and is well illustrated with worked examples and diagrams.
New edition of a successful undergraduate guide to the basics of an important mathematical technique.
Table of contents:
1. Physics and Fourier transforms; 2. Useful properties and theorems; 3. Applications I: Fraunhofer diffraction; 4. Applications II: communication theory; 5. Applications III: spectroscopy; 6. Two-dimensional transforms; 7. Multi-dimensional transforms; 8. The formal complex Fourier transform; 9. Discrete and digital Fourier transforms; Appendix: mathematical proofs.
A new edition of a successful textbook for students in physics, computer science and electrical engineering. Important ideas in practical science and information technology are described at an understandable level. The book covers the field broadly and is well illustrated with worked examples and diagrams.
New edition of a successful undergraduate guide to the basics of an important mathematical technique.