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  3. A Student's Guide to Fourier Transforms
  • Cited by 10
      • 2nd edition
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2012
      September 2002
      ISBN:
      9781139164917
      DOI:
      https://doi.org/10.1017/CBO9781139164917
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      • Subjects:
      Physics and Astronomy, Engineering, General and Classical Physics, Engineering Mathematics and Programming
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    Subjects:
    Physics and Astronomy, Engineering, General and Classical Physics, Engineering Mathematics and Programming
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    Book description

    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.

    Reviews

    From reviews of the first edition:‘… elegantly simple.’

    Source: 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.’

    Source: Computers in Physics

    ‘… this is an excellent book to initiate students who possess a reasonable mathematical background to the use of Fourier transforms …’

    Source: Microscopy and Analysis

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    Contents

    Contents
    References
    Bibliography
    Abramowitz, M. and Stegun, I. A. Handbook of Mathematical Functions. Dover, New York. 1965
    Abramowitz, M. and Stegun, I. A. A more up-to-date version of Jahnke & Emde, below
    Bracewell, R. N. The Fourier Transform and its Applications. McGraw-Hill, New York. 1965
    Bracewell, R. N. This is one of the two most popular books on the subject. Similar in scope to this book, but more thorough and comprehensive
    Brigham, E. O. The Fast Fourier Transform. Prentice Hall, New York. 1974
    Brigham, E. O. The standard work on digital Fourier transforms and their implementation by various kinds of FFT programs
    Champeney, D. C. Fourier Transforms and Their Physical Applications. Academic Press, London and New York. 1973
    Champeney, D. C. Like Bracewell, one of the two most popular books on practical Fourier tranforming. Covers similar ground, but with some differences
    Champeney, D. C. A Handbook of Fourier Theorems. Cambridge University Press. 1987
    Herman, Gabor T. Image Reconstruction From Projections. Academic Press, London and New York. 1980
    Herman, Gabor T. Includes details of Fourier methods (among others) for computerized tomography, including theory and applications
    Jahnke, E and Emde, F. Tables of Functions with Formulae and Curves. Dover, New York. 1943
    Jahnke, E and Emde, F. The classic work on the functions of mathematical physics, with diagrams, charts and tables, of Bessel functions, Legendre polynomials, spherical harmonics etc
    Körner, T. W. Fourier Analysis. Cambridge University Press. 1988
    Körner, T. W. One of the more thorough and entertaining works on analytic Fourier theory, but plenty of physical applications: expensive, but firmly recommended for serious students
    Titchmarsh, E. C. An Introduction to the theory of Fourier Integrals. Clarendon Press, Oxford. 1962
    Titchmarsh, E. C. The theorists' standard work on Fourier theory. Unnecessarily difficult for ordinary mortals, but needs consulting occasionally
    Watson, G. N. A Treatise of the Theory of Bessel Functions, Cambridge University Press. 1962
    Watson, G. N. Another great theoretical classic: chiefly for consultation by people who have equations they can't solve, and which seem likely to involve Bessel functions
    Whittaker, J. M. Interpolary Function Theory, Cambridge University Press. 1935
    Whittaker, J. M. A slim volume dealing with (among other things) the sampling theorem and problems of interpolating points between samples of band-limited curves

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