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From Fourier Analysis to Wavelets

  • Jonas Gomes
  • Luiz Velho

Part of the IMPA Monographs book series (IMPA, volume 3)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jonas Gomes, Luiz Velho
    Pages 1-11
  3. Jonas Gomes, Luiz Velho
    Pages 13-27
  4. Jonas Gomes, Luiz Velho
    Pages 29-46
  5. Jonas Gomes, Luiz Velho
    Pages 47-60
  6. Jonas Gomes, Luiz Velho
    Pages 61-73
  7. Jonas Gomes, Luiz Velho
    Pages 75-88
  8. Jonas Gomes, Luiz Velho
    Pages 89-100
  9. Jonas Gomes, Luiz Velho
    Pages 101-112
  10. Jonas Gomes, Luiz Velho
    Pages 113-125
  11. Jonas Gomes, Luiz Velho
    Pages 127-141
  12. Jonas Gomes, Luiz Velho
    Pages 143-155
  13. Jonas Gomes, Luiz Velho
    Pages 157-177
  14. Jonas Gomes, Luiz Velho
    Pages 179-183
  15. Back Matter
    Pages 185-210

About this book

Introduction

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.

Keywords

Fourier Analysis Fourier Transform Function Representation Wavelet Design Wavelet Transform Wavelets

Authors and affiliations

  • Jonas Gomes
    • 1
  • Luiz Velho
    • 2
  1. 1.Offices Shopping LeblonBOZANO InvestimentosRio de JaneiroBrazil
  2. 2.Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil

Bibliographic information