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1.

図書
図書
1. Wavelet methods for time series analysis
Donald B. Percival, Andrew T. Walden
出版情報: Cambridge : Cambridge University Press, 2000  xxv, 594 p. ; 27 cm
シリーズ名: Cambridge series on statistical and probabilistic mathematics
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目次情報: 続きを見る
Introduction to wavelets / 1：
Review of Fourier theory and filters / 2：
Orthonormal transforms of time series / 3：
The discrete wavelet transform / 4：
The maximal overlap discrete wavelet transform / 5：
The discrete wavelet packet transform / 6：
Random variables and stochastic processes / 7：
The wavelet variance / 8：
Analysis and synthesis of long memory processes / 9：
Wavelet-based signal estimation / 10：
Wavelet analysis of finite energy signals / 11：
Appendix. Answers to embedded exercises
References
Author index
Subject index
Introduction to wavelets / 1：
Review of Fourier theory and filters / 2：
Orthonormal transforms of time series / 3：
2.

図書
図書
2. Complex harmonic splines, periodic quasi-wavelets : theory and applications
by Han-lin Chen
出版情報: Dordrecht ; Boston : Kluwer Academic, c2000  xii, 226 p. ; 25 cm
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3.

図書
図書
3. Fourier and wavelet analysis
George Bachman, Lawrence Narici, Edward Beckenstein
出版情報: New York : Springer, c2000  ix, 505 p. ; 25 cm
シリーズ名: Universitext
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4.

図書
図書
4. Introduction to Fourier analysis and wavelets
Mark A. Pinsky
出版情報: Australia : Brooks/Cole, c2002  xviii, 376 p. ; 25 cm
シリーズ名: Brooks/Cole series in advanced mathematics
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目次情報: 続きを見る
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
The Vibrating String / 1.1.1.1：
Heat Flow in Solids / 1.1.1.2：
Absolutely Convergent Trigonometric Series / 1.1.2：
Examples of Factorial and Bessel Functions / 1.1.3：
Poisson Kernel Example / 1.1.4：
Proof of Laplace's Method / 1.1.5：
Nonabsolutely Convergent Trigonometric Series / 1.1.6：
Formulation of Fourier Series / 1.2：
Fourier Coefficients and Their Basic Properties / 1.2.1：
Fourier Series of Finite Measures / 1.2.2：
Rates of Decay of Fourier Coefficients / 1.2.3：
Piecewise Smooth Functions / 1.2.3.1：
Fourier Characterization of Analytic Functions / 1.2.3.2：
Sine Integral / 1.2.4：
Other Proofs That Si([infinity]) = 1 / 1.2.4.1：
Pointwise Convergence Criteria / 1.2.5：
Integration of Fourier Series / 1.2.6：
Convergence of Fourier Series of Measures / 1.2.6.1：
Riemann Localization Principle / 1.2.7：
Gibbs-Wilbraham Phenomenon / 1.2.8：
The General Case / 1.2.8.1：
Fourier Series in L[superscript 2] / 1.3：
Mean Square Approximation--Parseval's Theorem / 1.3.1：
Application to the Isoperimetric Inequality / 1.3.2：
Rates of Convergence in L[superscript 2] / 1.3.3：
Application to Absolutely-Convergent Fourier Series / 1.3.3.1：
Norm Convergence and Summability / 1.4：
Approximate Identities / 1.4.1：
Almost-Everywhere Convergence of the Abel Means / 1.4.1.1：
Summability Matrices / 1.4.2：
Fejer Means of a Fourier Series / 1.4.3：
Wiener's Closure Theorem on the Circle / 1.4.3.1：
Equidistribution Modulo One / 1.4.4：
Hardy's Tauberian Theorem / 1.4.5：
Improved Trigonometric Approximation / 1.5：
Rates of Convergence in C (T) / 1.5.1：
Approximation with Fejer Means / 1.5.2：
Jackson's Theorem / 1.5.3：
Higher-Order Approximation / 1.5.4：
Converse Theorems of Bernstein / 1.5.5：
Divergence of Fourier Series / 1.6：
The Example of du Bois-Reymond / 1.6.1：
Analysis via Lebesgue Constants / 1.6.2：
Divergence in the Space L[superscript 1] / 1.6.3：
Appendix: Complements on Laplace's Method / 1.7：
First Variation on the Theme-Gaussian Approximation / 1.7.0.1：
Second Variation on the Theme-Improved Error Estimate / 1.7.0.2：
Application to Bessel Functions / 1.7.1：
The Local Limit Theorem of DeMoivre-Laplace / 1.7.2：
Appendix: Proof of the Uniform Boundedness Theorem / 1.8：
Appendix: Higher-Order Bessel functions / 1.9：
Appendix: Cantor's Uniqueness Theorem / 1.10：
Fourier Transforms on the Line And Space / 2：
Basic Properties of the Fourier Transform / 2.1：
Riemann-Lebesgue Lemma / 2.2.1：
Approximate Identities and Gaussian Summability / 2.2.2：
Improved Approximate Identities for Pointwise Convergence / 2.2.2.1：
Application to the Fourier Transform / 2.2.2.2：
The n-Dimensional Poisson Kernel / 2.2.2.3：
Fourier Transforms of Tempered Distributions / 2.2.3：
Characterization of the Gaussian Density / 2.2.4：
Wiener's Density Theorem / 2.2.5：
Fourier Inversion in One Dimension / 2.3：
Dirichlet Kernel and Symmetric Partial Sums / 2.3.1：
Example of the Indicator Function / 2.3.2：
Dini Convergence Theorem / 2.3.3：
Extension to Fourier's Single Integral / 2.3.4.1：
Smoothing Operations in R[superscript 1]-Averaging and Summability / 2.3.5：
Averaging and Weak Convergence / 2.3.6：
Cesaro Summability / 2.3.7：
Approximation Properties of the Fejer Kernel / 2.3.7.1：
Bernstein's Inequality / 2.3.8：
One-Sided Fourier Integral Representation / 2.3.9：
Fourier Cosine Transform / 2.3.9.1：
Fourier Sine Transform / 2.3.9.2：
Generalized h-Transform / 2.3.9.3：
L[superscript 2] Theory in R[superscript n] / 2.4：
Plancherel's Theorem / 2.4.1：
Bernstein's Theorem for Fourier Transforms / 2.4.2：
The Uncertainty Principle / 2.4.3：
Uncertainty Principle on the Circle / 2.4.3.1：
Spectral Analysis of the Fourier Transform / 2.4.4：
Hermite Polynomials / 2.4.4.1：
Eigenfunction of the Fourier Transform / 2.4.4.2：
Orthogonality Properties / 2.4.4.3：
Completeness / 2.4.4.4：
Spherical Fourier Inversion in R[superscript n] / 2.5：
Bochner's Approach / 2.5.1：
Piecewise Smooth Viewpoint / 2.5.2：
Relations with the Wave Equation / 2.5.3：
The Method of Brandolini and Colzani / 2.5.3.1：
Bochner-Riesz Summability / 2.5.4：
A General Theorem on Almost-Everywhere Summability / 2.5.4.1：
Bessel Functions / 2.6：
Fourier Transforms of Radial Functions / 2.6.1：
L[superscript 2]-Restriction Theorems for the Fourier Transform / 2.6.2：
An Improved Result / 2.6.2.1：
Limitations on the Range of p / 2.6.2.2：
The Method of Stationary Phase / 2.7：
Statement of the Result / 2.7.1：
Proof of the Method of Stationary Phase / 2.7.2：
Abel's Lemma / 2.7.4：
Fourier Analysis in L[superscript p] Spaces / 3：
The M. Riesz-Thorin Interpolation Theorem / 3.1：
Generalized Young's Inequality / 3.2.0.1：
The Hausdorff-Young Inequality / 3.2.0.2：
Stein's Complex Interpolation Theorem / 3.2.1：
The Conjugate Function or Discrete Hilbert Transform / 3.3：
L[superscript p] Theory of the Conjugate Function / 3.3.1：
L[superscript 1] Theory of the Conjugate Function / 3.3.2：
Identification as a Singular Integral / 3.3.2.1：
The Hilbert Transform on R / 3.4：
L[superscript 2] Theory of the Hilbert Transform / 3.4.1：
L[superscript p] Theory of the Hilbert Transform, 1 [ p [ [infinity] / 3.4.2：
Applications to Convergence of Fourier Integrals / 3.4.2.1：
L[superscript 1] Theory of the Hilbert Transform and Extensions / 3.4.3：
Kolmogorov's Inequality for the Hilbert Transform / 3.4.3.1：
Application to Singular Integrals with Odd Kernels / 3.4.4：
Hardy-Littlewood Maximal Function / 3.5：
Application to the Lebesgue Differentiation Theorem / 3.5.1：
Application to Radial Convolution Operators / 3.5.2：
Maximal Inequalities for Spherical Averages / 3.5.3：
The Marcinkiewicz Interpolation Theorem / 3.6：
Calderon-Zygmund Decomposition / 3.7：
A Class of Singular Integrals / 3.8：
Properties of Harmonic Functions / 3.9：
General Properties / 3.9.1：
Representation Theorems in the Disk / 3.9.2：
Representation Theorems in the Upper Half-Plane / 3.9.3：
Herglotz/Bochner Theorems and Positive Definite Functions / 3.9.4：
Poisson Summation Formula And Multiple Fourier Series / 4：
The Poisson Summation Formula in R[superscript 1] / 4.1：
Periodization of a Function / 4.2.1：
Statement and Proof / 4.2.2：
Shannon Sampling / 4.2.3：
Multiple Fourier Series / 4.3：
Basic L[superscript 1] Theory / 4.3.1：
Pointwise Convergence for Smooth Functions / 4.3.1.1：
Representation of Spherical Partial Sums / 4.3.1.2：
Basic L[superscript 2] Theory / 4.3.2：
Restriction Theorems for Fourier Coefficients / 4.3.3：
Poisson Summation Formula in R[superscript d] / 4.4：
Simultaneous Nonlocalization / 4.4.1：
Application to Lattice Points / 4.5：
Kendall's Mean Square Error / 4.5.1：
Landau's Asymptotic Formula / 4.5.2：
Application to Multiple Fourier Series / 4.5.3：
Three-Dimensional Case / 4.5.3.1：
Higher-Dimensional Case / 4.5.3.2：
Schrodinger Equation and Gauss Sums / 4.6：
Distributions on the Circle / 4.6.1：
The Schrodinger Equation on the Circle / 4.6.2：
Recurrence of Random Walk / 4.7：
Applications to Probability Theory / 5：
Basic Definitions / 5.1：
The Central Limit Theorem / 5.2.1：
Restatement in Terms of Independent Random Variables / 5.2.1.1：
Extension to Gap Series / 5.3：
Extension to Abel Sums / 5.3.1：
Weak Convergence of Measures / 5.4：
An Improved Continuity Theorem / 5.4.1：
Another Proof of Bochner's Theorem / 5.4.1.1：
Convolution Semigroups / 5.5：
The Berry-Esseen Theorem / 5.6：
Extension to Different Distributions / 5.6.1：
The Law of the Iterated Logarithm / 5.7：
Introduction to Wavelets / 6：
Heuristic Treatment of the Wavelet Transform / 6.1：
Wavelet Transform / 6.2：
Wavelet Characterization of Smoothness / 6.2.0.1：
Haar Wavelet Expansion / 6.3：
Haar Functions and Haar Series / 6.3.1：
Haar Sums and Dyadic Projections / 6.3.2：
Completeness of the Haar Functions / 6.3.3：
Haar Series in C[subscript 0] and L[subscript p] Spaces / 6.3.3.1：
Pointwise Convergence of Haar Series / 6.3.3.2：
Construction of Standard Brownian Motion / 6.3.4：
Haar Function Representation of Brownian Motion / 6.3.5：
Proof of Continuity / 6.3.6：
Levy's Modulus of Continuity / 6.3.7：
Multiresolution Analysis / 6.4：
Orthonormal Systems and Riesz Systems / 6.4.1：
Scaling Equations and Structure Constants / 6.4.2：
From Scaling Function to MRA / 6.4.3：
Additional Remarks / 6.4.3.1：
Meyer Wavelets / 6.4.4：
From Scaling Function to Orthonormal Wavelet / 6.4.5：
Direct Proof that V[subscript 1] [minus sign in circle] V[subscript 0] Is Spanned by {[Psi](t - k)}[subscript k[set membership]Z] / 6.4.5.1：
Null Integrability of Wavelets Without Scaling Functions / 6.4.5.2：
Wavelets with Compact Support / 6.5：
From Scaling Filter to Scaling Function / 6.5.1：
Explicit Construction of Compact Wavelets / 6.5.2：
Daubechies Recipe / 6.5.2.1：
Hernandez-Weiss Recipe / 6.5.2.2：
Smoothness of Wavelets / 6.5.3：
A Negative Result / 6.5.3.1：
Cohen's Extension of Theorem 6.5.1 / 6.5.4：
Convergence Properties of Wavelet Expansions / 6.6：
Wavelet Series in L[superscript p] Spaces / 6.6.1：
Large Scale Analysis / 6.6.1.1：
Almost-Everywhere Convergence / 6.6.1.2：
Convergence at a Preassigned Point / 6.6.1.3：
Jackson and Bernstein Approximation Theorems / 6.6.2：
Wavelets in Several Variables / 6.7：
Two Important Examples / 6.7.1：
Tensor Product of Wavelets / 6.7.1.1：
General Formulation of MRA and Wavelets in R[superscript d] / 6.7.2：
Notations for Subgroups and Cosets / 6.7.2.1：
Riesz Systems and Orthonormal Systems in R[superscript d] / 6.7.2.2：
Scaling Equation and Structure Constants / 6.7.2.3：
Existence of the Wavelet Set / 6.7.2.4：
Proof That the Wavelet Set Spans V[subscript 1] [minus sign in circle] V[subscript 0] / 6.7.2.5：
Cohen's Theorem in R[superscript d] / 6.7.2.6：
Examples of Wavelets in R[superscript d] / 6.7.3：
References
Notations
Index
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
5.

図書
図書
5. Wavelets and signal processing
Lokenath Debnath, editor
出版情報: Boston : Birkhäuser, c2003  xxv, 435 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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6.

図書
図書
6. Wavelets and multiwavelets
Fritz Keinert
出版情報: Boca Raton : Chapman & Hall/CRC, c2004  xii, 275 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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7.

図書
図書
7. Nonlinear hyperbolic equations, spectral theory, and wavelet transformations : a volume of advances in partial differential equations (:us ; :sz)
Sergio Albeverio ... [et al], editors
出版情報: Basel : Birkhäuser, c2003  [vii], 437 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 145
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8.

図書
図書
8. Wavelet transforms and time-frequency signal analysis
Lokenath Debnath, editor
出版情報: Boston : Birkhäuser, c2001  xx, 423 p., [8] p. of plates ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface Contributors Color Insert
Wavelets and Wavelet / I：
Transforms Wavelet Frames: Multiresolution Analysis and Extension Principles / J.J. Benedetto ; O.M. Treiber
Convergence Rates of Multiscale and Wavelet Expansions / M.A. Kon ; L.A. Raphael Denoising via
Nonorthogonal Wavelet Transforms / K. Berkner ; R.O. Wells ; Jr. Osiris
Wavelets and the Dipole Gas / G. Battle
Wavelets in Closed Forms / A. Zayed ; G.G. Walter
Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods / C. PFrez ; R. Schneider
Computing and Analyzing Turbulent Flows Using Wavelets / K. Schneider ; M. Farge
The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform / L. Cohen
Time-Frequency Signal Analysis Quadratic Time-Frequency Analysis of Linear, Time-Varying Systems / F. Hlawatsch ; G. MatzII：
Inequalities in Mellin--Fourier Signal Analysis / P. Flandrin
Introduction to Time-Frequency Signal Analysis / B. Boashash ; B. Barkat
Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations / W.J. Williams
Index
Preface Contributors Color Insert
Wavelets and Wavelet / I：
Transforms Wavelet Frames: Multiresolution Analysis and Extension Principles / J.J. Benedetto ; O.M. Treiber
9.

図書
図書
9. Wavelets and subbands : fundamentals and applications
Agostino Abbate, Casimer M. DeCusatis, Pankaj K. Das
出版情報: Boston : Birkhäuser, c2002  xvii, 551 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface
Notation
Introduction / 1.：
Historical Review: From Fourier Analysis to Wavelet Analysis and Subband / 1.1：
Organization of This Book / 1.2：
References / 1.3：
Fundamentals / Part I：
Wavelet Fundamentals / 2.：
Why Wavelet Transforms? / 2.1：
Fourier Transform as a Wave Transform / 2.3：
Wavelet Transform / 2.4：
Connection Between Wavelets and Filters / 2.5：
Time-Frequency Analysis: Short-Time Fourier Transform, Gabor Transform, and Tiling in the Time-Frequency Plane / 2.6：
Examples of Wavelets / 2.7：
From the Continuous to the Discrete Case / 2.8：
Frames / 2.9：
Subbands / 2.10：
Multiresolution Analysis / 2.11：
Matrix Formulation / 2.12：
Multiresolution Revisited / 2.13：
Two-Dimensional Case / 2.14：
DWT and Subband Example / 2.15：
Implementations / 2.16：
Summary and Conclusions / 2.17：
Wavelets and Subbands / 2.18：
Time and Frequency Analysis of Signals / 3.：
Fundamentals of Signal Analysis / 3.1：
Uncertainty Principle / 3.1.2：
Windowed Fourier Transform: Short-Time Fourier Transform and Gabor Transform / 3.2：
General Properties of the Windowed Fourier Transform / 3.2.1：
Uncertainty Principle for Windowed Fourier Transform / 3.2.2：
Inverse Windowed Fourier Transform / 3.2.3：
Continuous Wavelet Transform / 3.3：
Mathematics of the Continuous Wavelet Transform / 3.3.1：
Properties of the Continuous Wavelet Transform / 3.3.2：
Inverse Wavelet Transform / 3.3.3：
Examples of Mother Wavelets / 3.3.4：
Analytic Wavelet Transform / 3.4：
Analytic Signals / 3.4.1：
Analytic Wavelet Transform on Real Signals / 3.4.2：
Physical Interpretation of an Analytic Signal / 3.4.3：
Quadratic Time-Frequency Distributions / 3.5：
Discrete Wavelet Transform: From Frames to Fast Wavelet Transform / 3.6：
Fundamentals of Frame Theory / 4.1：
Sampling Theorem / 4.3：
Wavelet Frames / 4.4：
Examples of Wavelet Frames / 4.5：
Time-Frequency Localization / 4.6：
Orthonormal Discrete Wavelet Transforms / 4.7：
Scaling Functions / 4.8：
Construction of Wavelet Bases Using Multiresolution Analysis / 4.10：
Wavelet Bases / 4.11：
Shannon Wavelet / 4.11.1：
Meyer Wavelet / 4.11.2：
Haar Wavelet / 4.11.3：
Battle-Lemarie (Spline) Wavelets / 4.11.4：
Daubechies Compactly Supported Wavelets / 4.12：
Fast Wavelet Transform / 4.13：
Biorthogonal Wavelet Bases / 4.14：
Theory of Subband Decomposition / 4.15：
Fundamentals of Digital Signal Processing / 5.1：
Multirate Systems / 5.3：
Polyphase Decomposition / 5.4：
Two-Channel Filter Bank/PR Filter / 5.5：
Biorthogonal Filters / 5.6：
Lifting Scheme / 5.7：
M-Band Case / 5.8：
Applications of Multirate Filtering / 5.9：
Two-Dimensional Wavelet Transforms and Applications / 5.10：
Orthogonal Pyramid Transforms / 6.1：
Progressive Transforms for Lossless and Lossy Image Coding / 6.3：
Embedded Zerotree Wavelets / 6.4：
Applications / 6.5：
Applications of Wavelets in the Analysis of Transient Signals / 7.：
Introduction to Time-Frequency Analysis of Transient Signals / 7.1：
Ultrasonic Systems / 7.2.1：
Ultrasonic Characterization of Coatings by the Ridges of the Analytic Wavelet Transform / 7.2.2：
Characterization of Coatings / 7.2.3：
Biomedical Application of Wavelets: Analysis of EEG Signals for Monitoring Depth of Anesthesia / 7.3：
Wavelet Spectral Analysis of EEG Signals / 7.3.1：
System Response Wavelet Analysis of EEG Signals / 7.3.2：
Discussion of Results / 7.3.3：
Applications of Subband and Wavelet Transform in Communication Systems / 7.4：
Applications in Spread Spectrum Communication Systems / 8.1：
Excision / 8.2.1：
Adaptive Filter-Bank Exciser / 8.2.2：
Transform-Based Low Probability of Intercept Receiver / 8.2.3：
Application of Multirate Filter Bank in Spreading Code Generation and Multiple Access / 8.2.4：
Modulation Using Filter Banks and Wavelets / 8.3：
Multitione Modulation / 8.4：
Noise Reduction in Audio and Images Using Wavelets / 8.5：
Audio/Video/Image Compression / 8.6：
Progressive Pattern Recognition
Real-Time Implementations of Wavelet Transforms / 8.7：
Digital VLSI Implementation / 9.1：
Optical Implementation / 9.2：
Matrix Processing and Neural Networks / 9.2.1：
Acousto-Optic Devices / 9.2.2：
Other Optical Implementations / 9.2.3：
Appendix / 9.3：
Fourier Transform / A.：
Discrete Fourier Transform / B.：
z-Transform / C.：
Orthogonal Representation of Signals / D.：
Bibliography
Index
Preface
Notation
Introduction / 1.：
10.

図書
図書
10. Wavelets in numerical simulation : problem adapted construction and applications
Karsten Urban
出版情報: Berlin : Springer, c2002  xv, 181 p. ; 24 cm
シリーズ名: Lecture notes in computational science and engineering ; 22
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