Discrete Fourier Analysis

• Κύριος συγγραφέας: Wong, M. W. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Springer Basel, 2011.
• Σειρά: Pseudo-Differential Operators, Theory and Applications ; 5
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.