Fourier Transforms

An Introduction for Engineers

  • Robert M. Gray
  • Joseph W. Goodman

Table of contents

  1. Front Matter
    Pages i-xx
  2. Robert M. Gray, Joseph W. Goodman
    Pages 1-51
  3. Robert M. Gray, Joseph W. Goodman
    Pages 53-113
  4. Robert M. Gray, Joseph W. Goodman
    Pages 115-160
  5. Robert M. Gray, Joseph W. Goodman
    Pages 161-215
  6. Robert M. Gray, Joseph W. Goodman
    Pages 217-250
  7. Robert M. Gray, Joseph W. Goodman
    Pages 251-307
  8. Robert M. Gray, Joseph W. Goodman
    Pages 309-332
  9. Robert M. Gray, Joseph W. Goodman
    Pages 333-345
  10. Back Matter
    Pages 347-361

About this book

Introduction

The Fourier transform is one of the most important mathematical tools in a wide variety of fields in science and engineering. In the abstract it can be viewed as the transformation of a signal in one domain (typically time or space) into another domain, the frequency domain. Applications of Fourier transforms, often called Fourier analysis or harmonic analysis, provide useful decompositions of signals into fundamental or "primitive" components, provide shortcuts to the computation of complicated sums and integrals, and often reveal hidden structure in data. Fourier analysis lies at the base of many theories of science and plays a fundamental role in practical engineering design. The origins of Fourier analysis in science can be found in Ptolemy's decomposing celestial orbits into cycles and epicycles and Pythagorus' de­ composing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J. Fourier in his 1822 Theorie analytique de la Chaleur [16] (still available as a Dover reprint) was the first to claim that arbitrary periodic functions could be expanded in a trigonometric (later called a Fourier) series, a claim that was eventually shown to be incorrect, although not too far from the truth. It is an amusing historical sidelight that this work won a prize from the French Academy, in spite of serious concerns expressed by the judges (Laplace, Lagrange, and Legendre) re­ garding Fourier's lack of rigor.

Keywords

Fourier analysis correlation harmonic analysis signal tables

Authors and affiliations

  • Robert M. Gray
    • 1
  • Joseph W. Goodman
    • 1
  1. 1.Information Systems Laboratory Department of Electrical EngineeringStanford UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-2359-8
  • Copyright Information Kluwer Academic Publishers 1995
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-6001-8
  • Online ISBN 978-1-4615-2359-8
  • Series Print ISSN 0893-3405
  • About this book