Discrete Fourier Analysis

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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Wong, M. W. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Basel : Springer Basel : Imprint: Birkhäuser, 2011.
Edition:1st ed. 2011.
Series:Pseudo-Differential Operators, Theory and Applications, 5
Subjects:
Fourier analysis.
Harmonic analysis.
Differential equations.
Numerical analysis.
Fourier Analysis.
Abstract Harmonic Analysis.
Differential Equations.
Numerical Analysis.
Online Access:Texto Completo
Table of Contents:
  • Preface
  • The Finite Fourier Transform
  • Translation-Invariant Linear Operators
  • Circulant Matrices
  • Convolution Operators
  • Fourier Multipliers
  • Eigenvalues and Eigenfunctions
  • The Fast Fourier Transform
  • Time-Frequency Analysis
  • Time-Frequency Localized Bases
  • Wavelet Transforms and Filter Banks
  • Haar Wavelets
  • Daubechies Wavelets
  • The Trace
  • Hilbert Spaces
  • Bounded Linear Operators
  • Self-Adjoint Operators
  • Compact Operators
  • The Spectral Theorem
  • Schatten-von Neumann Classes
  • Fourier Series
  • Fourier Multipliers on S1
  • Pseudo-Differential Operators on S1
  • Pseudo-Differential Operators on Z
  • Bibliography
  • Index.

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