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Fourier Techniques and Applications

  • Book
  • © 1985

Overview

Editors:
  1. John F. Price

    1. School of Mathematics, University of New South Wales, Kensington, Australia

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-viii
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  2. The Life of Joseph Fourier

    1. The Life of Joseph Fourier

      • R. N. Bracewell
      Pages 1-4

  3. Applied Fourier Analysis

    1. Front Matter

      Pages 5-5
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    2. Linear Systems, Filters and Convolution Theorems

      • J. W. Sanders
      Pages 7-24

    3. Uncertainty Principles and Sampling Theorems

      • John F. Price
      Pages 25-44

    4. Fourier Techniques in Two Dimensions

      • R. N. Bracewell
      Pages 45-71

    5. Some Mathematical Methods for Spectrum Estimation

      • John J. Benedetto
      Pages 73-100

    6. Some Practical and Statistical Aspects of Filtering and Spectrum Estimation

      • T. P. Speed
      Pages 101-118

  4. Fourier Techniques and Applications

    1. Front Matter

      Pages 119-119
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    2. Two-Dimensional Phase Restoration

      • R. H. T. Bates, W. R. Fright
      Pages 121-148

    3. Fourier Uniqueness Criteria And Spectrum Estimation Theorems

      • John J. Benedetto
      Pages 149-170

    4. Harmonic Synthesis — Theoretical Bounds

      • Gavin Brown
      Pages 171-181

    5. Seismic Image Processing for Petroleum Exploration

      • P. W. Buchen
      Pages 183-183

    6. Fourier Theory in Modern Imaging

      • T. W. Cole
      Pages 185-199

    7. An Overview of Time and Frequency Limiting

      • H. J. Landau
      Pages 201-220

    8. From Rainbows to Rings: A History of the Idea of the Spectrum

      • D. E. Taylor
      Pages 221-224

  5. Back Matter

    Pages 225-231
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Keywords

About this book

The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera­ ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis­ tribution was sinusoidal. He then asserted that any distri­ bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu­ tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua non of Fourier analysis and synthesis, has led to the routine use of the methods originating with Fourier in a great diversity of areas - astrophysics, computing, economics, electrical engineering, geophysics, information theory, medical engineering, optics, petroleum and mineral exploration, quan­ tum physics and spectroscopy, to name a few.

Editors and Affiliations

  • School of Mathematics, University of New South Wales, Kensington, Australia

    John F. Price

Bibliographic Information

  • Book Title: Fourier Techniques and Applications

  • Editors: John F. Price

  • DOI: https://doi.org/10.1007/978-1-4613-2525-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Plenum Press, New York 1985

  • Hardcover ISBN: 978-0-306-42100-6Due: 01 October 1985

  • Softcover ISBN: 978-1-4612-9525-9Published: 16 September 2011

  • eBook ISBN: 978-1-4613-2525-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: 231

  • Topics: Mathematics, general, Chemistry/Food Science, general

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