IMPA Monographs

From Fourier Analysis to Wavelets

Authors: Gomes, Jonas, Velho, Luiz

  • Includes extensive appendices on Systems and Filters and the Z Transform
  • Emphasis is given on ideas and intuition rather than heavy computations
  • Provides great detail on different types of wavelets: Orthogonal Wavelets, Biorthogonal Wavelets, Wavelet Design, and Constructing Wavelets
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eBook $69.99
price for Brazil (gross)
  • ISBN 978-3-319-22075-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for Brazil
  • ISBN 978-3-319-22074-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for Brazil
  • ISBN 978-3-319-37022-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed.

Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets.  Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable.

This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

Reviews

“The authors present a short textbook about the fundamentals of Fourier analysis (such as Fourier series, Fourier transform, and windowed Fourier transform) and wavelet theory (such as continuous/discrete wavelet transforms, multiresolution analysis, decomposition/reconstruction algorithms, and construction of orthogonal/biorthogonal wavelets) with emphasis on the underlying ideas. … This textbook is mainly written for students in computer science, physics, and engineering.” (Manfred Tasche, zbMATH, Vol. 1325.42001, 2016)


Table of contents (13 chapters)

Buy this book

eBook $69.99
price for Brazil (gross)
  • ISBN 978-3-319-22075-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for Brazil
  • ISBN 978-3-319-22074-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for Brazil
  • ISBN 978-3-319-37022-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
From Fourier Analysis to Wavelets
Authors
Series Title
IMPA Monographs
Series Volume
3
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-22075-8
DOI
10.1007/978-3-319-22075-8
Hardcover ISBN
978-3-319-22074-1
Softcover ISBN
978-3-319-37022-4
Edition Number
1
Number of Pages
XIII, 210
Number of Illustrations and Tables
77 b/w illustrations
Topics