Discrete Fourier Analysis

• Main Author: Wong, M. W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2011.
• Series: Pseudo-Differential Operators, Theory and Applications ; 5
• Subjects: Mathematics.; Harmonic analysis.; Fourier analysis.; Partial differential equations.; Numerical analysis.; Fourier Analysis.; Abstract Harmonic Analysis.; Partial Differential Equations.; Numerical 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...

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.