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  • Textbook
  • Apr 2014

Fourier Analysis and Applications

Filtering, Numerical Computation, Wavelets

Part of the book series: Texts in Applied Mathematics (TAM, volume 30)

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Table of contents (42 chapters)

  1. Front Matter

    Pages i-xviii
  2. Signals and Systems

    1. Front Matter

      Pages 1-1
    2. Signals and Systems

      • Claude Gasquet, Patrick Witomski
      Pages 3-10
    3. Filters and Transfer Functions

      • Claude Gasquet, Patrick Witomski
      Pages 11-19
  3. Periodic Signals

    1. Front Matter

      Pages 21-21
    2. Trigonometric Signals

      • Claude Gasquet, Patrick Witomski
      Pages 23-26
    3. Periodic Signals and Fourier Series

      • Claude Gasquet, Patrick Witomski
      Pages 27-37
    4. Pointwise Representation

      • Claude Gasquet, Patrick Witomski
      Pages 39-50
    5. Expanding a Function in an Orthogonal Basis

      • Claude Gasquet, Patrick Witomski
      Pages 51-56
    6. Frequencies, Spectra, and Scales

      • Claude Gasquet, Patrick Witomski
      Pages 57-62
  4. The Discrete Fourier Transform and Numerical Computations

    1. Front Matter

      Pages 63-63
    2. The Discrete Fourier Transform

      • Claude Gasquet, Patrick Witomski
      Pages 65-73
    3. A Famous, Lightning-Fast Algorithm

      • Claude Gasquet, Patrick Witomski
      Pages 75-84
    4. Using the FFT for Numerical Computations

      • Claude Gasquet, Patrick Witomski
      Pages 85-94
  5. The Lebesgue Integral

    1. Front Matter

      Pages 95-95
    2. From Riemann to Lebesgue

      • Claude Gasquet, Patrick Witomski
      Pages 97-100
    3. Measuring Sets

      • Claude Gasquet, Patrick Witomski
      Pages 101-109
    4. Integrating Measurable Functions

      • Claude Gasquet, Patrick Witomski
      Pages 111-120
    5. Integral Calculus

      • Claude Gasquet, Patrick Witomski
      Pages 121-130
  6. Spaces

    1. Front Matter

      Pages 131-131

Reviews

From the reviews:

BULLETIN OF MATHEMATICS BOOKS

"This book should have wide appeal, from those who are just getting into the area and wish to learn mathematical foundations and applications to those who are already experienced and wish to have a reference that provides a mathematically rigorous coverage of the state of the art…The coverage is thorough but not overwhelming, perhaps because the chapters are divided into lessons, allowing the reader a chance to pause and think. The authors work clearly to impart an understanding of the theory and applications, and not just offer an encyclopedic tome."

Authors and Affiliations

  • Université Joseph Fourier (Grenoble I), France

    Claude Gasquet

  • Laboratoire LMC-IMAG, Tour IRMA, Grenoble, Cedex 09, France

    Patrick Witomski

Bibliographic Information