Skip to main content
  • Textbook
  • © 2011

Discrete Fourier Analysis

Birkhäuser

Authors:

  • The mathematical notions are presented both on a basic level, making thus the content accessible to a wide audience, and later on, on a more sophisticated level, which can bring students more effectively to the frontier of research
  • Pseudo-differential operators are presented in the perspectives of signal analysis
  • Exercises are included to enhance the use of the book as a textbook
  • Includes introduction to wavelets and to pseudo-differential operators

Part of the book series: Pseudo-Differential Operators (PDO, volume 5)

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (23 chapters)

  1. Front Matter

    Pages i-viii
  2. The Finite Fourier Transform

    • M. W. Wong
    Pages 1-16
  3. Circulant Matrices

    • M. W. Wong
    Pages 23-25
  4. Convolution Operators

    • M. W. Wong
    Pages 27-31
  5. Fourier Multipliers

    • M. W. Wong
    Pages 33-36
  6. Eigenvalues and Eigenfunctions

    • M. W. Wong
    Pages 37-39
  7. The Fast Fourier Transform

    • M. W. Wong
    Pages 41-43
  8. Time-Frequency Analysis

    • M. W. Wong
    Pages 45-51
  9. Time-Frequency Localized Bases

    • M. W. Wong
    Pages 53-59
  10. Wavelet Transforms and Filter Banks

    • M. W. Wong
    Pages 61-66
  11. Haar Wavelets

    • M. W. Wong
    Pages 67-78
  12. Daubechies Wavelets

    • M. W. Wong
    Pages 79-86
  13. The Trace

    • M. W. Wong
    Pages 87-94
  14. Hilbert Spaces

    • M. W. Wong
    Pages 95-106
  15. Bounded Linear Operators

    • M. W. Wong
    Pages 107-112
  16. Self-Adjoint Operators

    • M. W. Wong
    Pages 113-116
  17. Compact Operators

    • M. W. Wong
    Pages 117-120
  18. The Spectral Theorem

    • M. W. Wong
    Pages 121-124
  19. Schatten–von Neumann Classes

    • M. W. Wong
    Pages 125-127

About this book

This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis.

 

The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis.

 

Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Authors and Affiliations

  • Department of Mathematics & Statistics, York University, Toronto, Canada

    M. W. Wong

About the author

M. W. Wong is currently Chair of Department of Mathematics and Statistics at York University, Toronto (Canada), past-President (2005-07 and 2007-09) of the International Society for Analysis, its Applications and Computation (ISAAC) and Director of the ISAAC Special Interest Group in Pseudo-Differential Operators (IGPDO).

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access