Discrete Fourier Analysis

Authors:

ISBN: 978-3-0348-0115-7 (Print) 978-3-0348-0116-4 (Online)

Table of contents (23 chapters)

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  1. Front Matter

    Pages i-viii

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    Book Chapter

    Pages 1-16

    The Finite Fourier Transform

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    Book Chapter

    Pages 17-21

    Translation-Invariant Linear Operators

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    Book Chapter

    Pages 23-25

    Circulant Matrices

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    Book Chapter

    Pages 27-31

    Convolution Operators

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    Pages 33-36

    Fourier Multipliers

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    Book Chapter

    Pages 37-39

    Eigenvalues and Eigenfunctions

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    Book Chapter

    Pages 41-43

    The Fast Fourier Transform

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    Book Chapter

    Pages 45-51

    Time-Frequency Analysis

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    Book Chapter

    Pages 53-59

    Time-Frequency Localized Bases

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    Book Chapter

    Pages 61-66

    Wavelet Transforms and Filter Banks

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    Book Chapter

    Pages 67-78

    Haar Wavelets

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    Book Chapter

    Pages 79-86

    Daubechies Wavelets

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    Book Chapter

    Pages 87-94

    The Trace

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    Book Chapter

    Pages 95-106

    Hilbert Spaces

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    Book Chapter

    Pages 107-112

    Bounded Linear Operators

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    Book Chapter

    Pages 113-116

    Self-Adjoint Operators

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    Book Chapter

    Pages 117-120

    Compact Operators

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    Book Chapter

    Pages 121-124

    The Spectral Theorem

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    Book Chapter

    Pages 125-127

    Schatten–von Neumann Classes

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    Book Chapter

    Pages 129-140

    Fourier Series

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