The Springer International Series in Engineering and Computer Science

Fourier Transforms

An Introduction for Engineers

Authors: Gray, Robert M., Goodman, Joseph

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About this Textbook

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.

Table of contents (8 chapters)

  • Signals and Systems

    Gray, Robert M. (et al.)

    Pages 1-51

    Preview Buy Chapter 30,19 €
  • The Fourier Transform

    Gray, Robert M. (et al.)

    Pages 53-113

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  • Fourier Inversion

    Gray, Robert M. (et al.)

    Pages 115-160

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  • Basic Properties

    Gray, Robert M. (et al.)

    Pages 161-215

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  • Generalized Transforms and Functions

    Gray, Robert M. (et al.)

    Pages 217-250

    Preview Buy Chapter 30,19 €

Buy this book

eBook 99,99 €
price for Spain (gross)
  • ISBN 978-1-4615-2359-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 130,99 €
price for Spain (gross)
  • ISBN 978-0-7923-9585-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 130,99 €
price for Spain (gross)
  • ISBN 978-1-4613-6001-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Fourier Transforms
Book Subtitle
An Introduction for Engineers
Authors
Series Title
The Springer International Series in Engineering and Computer Science
Series Volume
322
Copyright
1995
Publisher
Springer US
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-1-4615-2359-8
DOI
10.1007/978-1-4615-2359-8
Hardcover ISBN
978-0-7923-9585-0
Softcover ISBN
978-1-4613-6001-8
Series ISSN
0893-3405
Edition Number
1
Number of Pages
XX, 361
Topics