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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Format: | eBook |
Language: | English |
Published: |
Basel
Springer Basel
2011, 2011
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Edition: | 1st ed. 2011 |
Series: | Pseudo-Differential Operators, Theory and Applications
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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