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

ISBN-10: 0521176832

ISBN-13: 9780521176835

Edition: 3rd 2011

Authors: J. F. James

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Description:

Fourier transform theory is of importance in a vast range of applications in physical science, engineering and applied mathematics. This text provides an introduction to the theory and practice of Fourier transforms.
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Book details

List price: $62.95
Edition: 3rd
Copyright year: 2011
Publisher: Cambridge University Press
Publication date: 3/31/2011
Binding: Paperback
Pages: 156
Size: 6.00" wide x 9.00" long x 0.25" tall
Weight: 0.748
Language: English

J. F. James has held teaching positions at The Queen's University, Belfast, and the University of Manchester, and is one of the pioneers of Fourier spectroscopy. He is the author of A Student's Guide to Fourier Transforms, now in its third edition, and Spectrograph Design Fundamentals (Cambridge University Press, 2011 and 2007 respectively).

Preface to the first edition
Preface to the second edition
Preface to the third edition
Physics and Fourier transforms
The qualitative approach
Fourier series
The amplitudes of the harmonics
Fourier transforms
Conjugate variables
Graphical representations
Useful functions
Worked examples
Useful properties and theorems
The Dirichlet conditions
Theorems
Convolutions and the convolution theorem
The algebra of convolutions
Odier theorems
Aliasing
Worked examples
Fraunhofer diffraction
Fraunhofer diffraction
Examples
Babinet's principle
Dipole arrays
Polar diagrams
Phase and coherence
Fringe visibility
The Michelson stellar interferometer
The van Cittert-Zernike theorem
signal analysis and communication theory
Communication channels
Noise
Filters
The matched filter theorem
Modulations
Multiplex transmission along a channel
The passage of some signals through simple filters
The Gibbs phenomenon
interference spectroscopy and spectral line shapes
Interference spectrometry
The Michelson multiplex spectrometer
The shapes of spectrum lines
Two-dimensional Fourier transforms
Cartesian coordinates
Polar coordinates
Theorems
Examples of two-dimensional Fourier transforms with circular symmetry
Applications
Solutions without circular symmetry
Multi-dimensional Fourier transforms
The Dirac wall
Computerized axial tomography
A 'spike' or 'nail'
The Dirac fence
The 'bed of nails'
Parallel-plane delta-functions
Point arrays
Lattices
The formal complex Fourier transform
Discrete and digital Fourier transforms
History
The discrete Fourier transform
The matrix form of the DFT
A BASIC FFT routine
Appendix
Bibliography
Index
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