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1.

図書

図書
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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2.

図書

図書
M.W. Wong
出版情報: Basel : Birkhäuser, c2002  vi, 156 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 136
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3.

図書

図書
Paul S. Addison
出版情報: Bristol : Institute of Physics Pub., c2002  xiii, 353 p., [8] p. of plates. ; 25 cm
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Preface
Getting started / 1:
Introduction / 1.1:
The wavelet transform / 1.2:
Reading the book / 1.3:
The continuous wavelet transform / 2:
The wavelet / 2.1:
Requirements for the wavelet / 2.3:
The energy spectrum of the wavelet / 2.4:
Identification of coherent structures / 2.5:
Edge detection / 2.7:
The inverse wavelet transform / 2.8:
The signal energy: wavelet-based energy and power spectra / 2.9:
The wavelet transform in terms of the Fourier transform / 2.10:
Complex wavelets: the Morlet wavelet / 2.11:
The wavelet transform, short time Fourier transform and Heisenberg boxes / 2.12:
Adaptive transforms: matching pursuits / 2.13:
Wavelets in two or more dimensions / 2.14:
The CWT: computation, boundary effects and viewing / 2.15:
Endnotes / 2.16:
Chapter keywords and phrases / 2.16.1:
Further resources / 2.16.2:
The discrete wavelet transform / 3:
Frames and orthogonal wavelet bases / 3.1:
Frames / 3.2.1:
Dyadic grid scaling and orthonormal wavelet transforms / 3.2.2:
The scaling function and the multiresolution representation / 3.2.3:
The scaling equation, scaling coefficients and associated wavelet equation / 3.2.4:
The Haar wavelet / 3.2.5:
Coefficients from coefficients: the fast wavelet transform / 3.2.6:
Discrete input signals of finite length / 3.3:
Approximations and details / 3.3.1:
The multiresolution algorithm--an example / 3.3.2:
Wavelet energy / 3.3.3:
Alternative indexing of dyadic grid coefficients / 3.3.4:
A simple worked example: the Haar wavelet transform / 3.3.5:
Everything discrete / 3.4:
Discrete experimental input signals / 3.4.1:
Smoothing, thresholding and denoising / 3.4.2:
Daubechies wavelets / 3.5:
Filtering / 3.5.1:
Symmlets and coiflets / 3.5.2:
Translation invariance / 3.6:
Biorthogonal wavelets / 3.7:
Two-dimensional wavelet transforms / 3.8:
Adaptive transforms: wavelet packets / 3.9:
Fluids / 3.10:
Statistical measures / 4.1:
Moments, energy and power spectra / 4.2.1:
Intermittency and correlation / 4.2.2:
Wavelet thresholding / 4.2.3:
Wavelet selection using entropy measures / 4.2.4:
Engineering flows / 4.3:
Jets, wakes, turbulence and coherent structures / 4.3.1:
Fluid-structure interaction / 4.3.2:
Two-dimensional flow fields / 4.3.3:
Geophysical flows / 4.4:
Atmospheric processes / 4.4.1:
Ocean processes / 4.4.2:
Other applications in fluids and further resources / 4.5:
Engineering testing, monitoring and characterization / 5:
Machining processes: control, chatter, wear and breakage / 5.1:
Rotating machinery / 5.3:
Gears / 5.3.1:
Shafts, bearings and blades / 5.3.2:
Dynamics / 5.4:
Chaos / 5.5:
Non-destructive testing / 5.6:
Surface characterization / 5.7:
Other applications in engineering and further resources / 5.8:
Impacting / 5.8.1:
Data compression / 5.8.2:
Engines / 5.8.3:
Miscellaneous / 5.8.4:
Medicine / 6:
The electrocardiogram / 6.1:
ECG timing, distortions and noise / 6.2.1:
Detection of abnormalities / 6.2.2:
Heart rate variability / 6.2.3:
Cardiac arrhythmias / 6.2.4:
ECG data compression / 6.2.5:
Neuroelectric waveforms / 6.3:
Evoked potentials and event-related potentials / 6.3.1:
Epileptic seizures and epileptogenic foci / 6.3.2:
Classification of the EEG using artificial neural networks / 6.3.3:
Pathological sounds, ultrasounds and vibrations / 6.4:
Blood flow sounds / 6.4.1:
Heart sounds and heart rates / 6.4.2:
Lung sounds / 6.4.3:
Acoustic response / 6.4.4:
Blood flow and blood pressure / 6.5:
Medical imaging / 6.6:
Ultrasonic images / 6.6.1:
Magnetic resonance imaging, computed tomography and other radiographic images / 6.6.2:
Optical imaging / 6.6.3:
Other applications in medicine / 6.7:
Electromyographic signals / 6.7.1:
Sleep apnoea / 6.7.2:
DNA / 6.7.3:
Fractals, finance, geophysics and other areas / 6.7.4:
Fractals / 7.1:
Exactly self-similar fractals / 7.2.1:
Stochastic fractals / 7.2.2:
Multifractals / 7.2.3:
Finance / 7.3:
Geophysics / 7.4:
Properties of subsurface media / 7.4.1:
Surface feature analysis / 7.4.2:
Climate, clouds, rainfall and river levels / 7.4.3:
Other areas / 7.5:
Astronomy / 7.5.1:
Chemistry and chemical engineering / 7.5.2:
Plasmas / 7.5.3:
Electrical systems / 7.5.4:
Sound and speech / 7.5.5:
Useful books, papers and websites / 7.5.6:
Useful books and papers
Useful websites
References
Index
Preface
Getting started / 1:
Introduction / 1.1:
4.

図書

図書
David F. Walnut
出版情報: Boston : Birkhäuser, c2002  xvii, 449 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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Preface
Preliminaries / Part I:
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
The Haar System / Part II:
The Discrete Haar Transform
Orthonormal Wavelet Bases / Part III:
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Other Wavelet Constructions / Part IV:
Biorthogonal Wavelets
Wavelet Packets
Applications / Part V:
Image Compression
Integral Operators
Review of Advanced Calculus and Linear Algebra / Appendix A:
Excursions in Wavelet Theory / Appendix B:
References Cited in the Text / Appendix C:
Index
Preface
Preliminaries / Part I:
Functions and Convergence
5.

図書

図書
Albert Boggess, Francis J. Narcowich
出版情報: Upper Saddle River, NJ : Prentice Hall, c2001  xix, 283 p. ; 25 cm
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Preface
Acknowledgments
Inner Product Spaces / 0:
Motivation / 0.1:
Definition of Inner Product / 0.2:
The Spaces L[superscript 2] and l[superscript 2] / 0.3:
Definitions / 0.3.1:
Convergence in L[superscript 2] versus Uniform Convergence / 0.3.2:
Schwarz and Triangle Inequalities / 0.4:
Orthogonality / 0.5:
Definitions and Examples / 0.5.1:
Orthogonal Projections / 0.5.2:
Gram-Schmidt Orthogonalization / 0.5.3:
Linear Operators and Their Adjoints / 0.6:
Linear Operators / 0.6.1:
Adjoints / 0.6.2:
Least Squares and Linear Predictive Coding / 0.7:
Best Fit Line for Data / 0.7.1:
General Least Squares Algorithm / 0.7.2:
Linear Predictive Coding / 0.7.3:
Exercises / 0.8:
Fourier Series / 1:
Introduction / 1.1:
Historical Perspective / 1.1.1:
Signal Analysis / 1.1.2:
Partial Differential Equations / 1.1.3:
Computation of Fourier Series / 1.2:
On the Interval -[pi] [less than or equal] x [less than or equal] [pi] / 1.2.1:
Other Intervals / 1.2.2:
Cosine and Sine Expansions / 1.2.3:
Examples / 1.2.4:
The Complex Form of Fourier Series / 1.2.5:
Convergence Theorems for Fourier Series / 1.3:
The Riemann-Lebesgue Lemma / 1.3.1:
Convergence at a Point of Continuity / 1.3.2:
Convergence at a Point of Discontinuity / 1.3.3:
Uniform Convergence / 1.3.4:
Convergence in the Mean / 1.3.5:
The Fourier Transform / 1.4:
Informal Development of the Fourier Transform / 2.1:
The Fourier Inversion Theorem / 2.1.1:
Properties of the Fourier Transform / 2.1.2:
Basic Properties / 2.2.1:
Fourier Transform of a Convolution / 2.2.2:
Adjoint of the Fourier Transform / 2.2.3:
Plancherel Formula / 2.2.4:
Linear Filters / 2.3:
Time Invariant Filters / 2.3.1:
Causality and the Design of Filters / 2.3.2:
The Sampling Theorem / 2.4:
The Uncertainty Principle / 2.5:
Discrete Fourier Analysis / 2.6:
The Discrete Fourier Transform / 3.1:
Definition of Discrete Fourier Transform / 3.1.1:
Properties of the Discrete Fourier Transform / 3.1.2:
The Fast Fourier Transform / 3.1.3:
The FFT Approximation to the Fourier Transform / 3.1.4:
Application--Parameter Identification / 3.1.5:
Application--Discretizations of Ordinary Differential Equations / 3.1.6:
Discrete Signals / 3.2:
Time Invariant, Discrete Linear Filters / 3.2.1:
Z-Transform and Transfer Functions / 3.2.2:
Haar Wavelet Analysis / 3.3:
Why Wavelets? / 4.1:
Haar Wavelets / 4.2:
The Haar Scaling Function / 4.2.1:
Basic Properties of the Haar Scaling Function / 4.2.2:
The Haar Wavelet / 4.2.3:
Haar Decomposition and Reconstruction Algorithms / 4.3:
Decomposition / 4.3.1:
Reconstruction / 4.3.2:
Filters and Diagrams / 4.3.3:
Summary / 4.4:
Multiresolution Analysis / 4.5:
The Multiresolution Framework / 5.1:
Definition / 5.1.1:
The Scaling Relation / 5.1.2:
The Associated Wavelet and Wavelet Spaces / 5.1.3:
Decomposition and Reconstruction Formulas: A Tale of Two Bases / 5.1.4:
Implementing Decomposition and Reconstruction / 5.1.5:
The Decomposition Algorithm / 5.2.1:
The Reconstruction Algorithm / 5.2.2:
Processing a Signal / 5.2.3:
Fourier Transform Criteria / 5.3:
The Scaling Function / 5.3.1:
Orthogonality via the Fourier Transform / 5.3.2:
The Scaling Equation via the Fourier Transform / 5.3.3:
Iterative Procedure for Constructing the Scaling Function / 5.3.4:
The Daubechies Wavelets / 5.4:
Daubechies's Construction / 6.1:
Classification, Moments, and Smoothness / 6.2:
Computational Issues / 6.3:
The Scaling Function at Dyadic Points / 6.4:
Other Wavelet Topics / 6.5:
Computational Complexity / 7.1:
Wavelet Algorithm / 7.1.1:
Wavelet Packets / 7.1.2:
Wavelets in Higher Dimensions / 7.2:
Relating Decomposition and Reconstruction / 7.3:
Transfer Function Interpretation / 7.3.1:
Wavelet Transform / 7.4:
Definition of the Wavelet Transform / 7.4.1:
Inversion Formula for the Wavelet Transform / 7.4.2:
Technical Matters / Appendix A:
Proof of the Fourier Inversion Formula / A.1:
Rigorous Proof of Theorem 5.17 / A.2:
Proof of Theorem 5.10 / A.2.1:
Proof of the Convergence Part of Theorem 5.23 / A.2.2:
Matlab Routines / Appendix B:
General Compression Routine / B.1:
Use of MATLAB's FFT Routine for Filtering and Compression / B.2:
Sample Routines Using MATLAB's Wavelet Toolbox / B.3:
MATLAB Code for the Algorithms in Section 5.2 / B.4:
Bibliography
Index
Preface
Acknowledgments
Inner Product Spaces / 0:
6.

図書

図書
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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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:
7.

図書

図書
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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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.:
8.

図書

図書
Hartmut Führ
出版情報: Berlin : Springer, c2005  x, 193 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1863
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目次情報: 続きを見る
Introduction / 1:
The Point of Departure / 1.1:
Overview of the Book / 1.2:
Preliminaries / 1.3:
Wavelet Transforms and Group Representations / 2:
Haar Measure and the Regular Representation / 2.1:
Coherent States and Resolutions of the Identity / 2.2:
Continuous Wavelet Transforms and the Regular Representation / 2.3:
Discrete Series Representations / 2.4:
Selfadjoint Convolution Idempotents and Support Properties / 2.5:
Discretized Transforms and Sampling / 2.6:
The Toy Example / 2.7:
The Plancherel Transform for Locally Compact Groups / 3:
A Direct Integral View of the Toy Example / 3.1:
Regularity Properties of Borel Spaces / 3.2:
Direct Integrals / 3.3:
Direct Integrals of Hilbert Spaces / 3.3.1:
Direct Integrals of von Neumann Algebras / 3.3.2:
Direct Integral Decomposition / 3.4:
The Dual and Quasi-Dual of a Locally Compact Group / 3.4.1:
Central Decompositions / 3.4.2:
Type I Representations and Their Decompositions / 3.4.3:
Measure Decompositions and Direct Integrals / 3.4.4:
The Plancherel Transform for Unimodular Groups / 3.5:
The Mackey Machine / 3.6:
Operator-Valued Integral Kernels / 3.7:
The Plancherel Formula for Nonunimodular Groups / 3.8:
The Plancherel Theorem / 3.8.1:
Construction Details / 3.8.2:
Plancherel Inversion and Wavelet Transforms / 4:
Fourier Inversion and the Fourier Algebra / 4.1:
Plancherel Inversion / 4.2:
Admissibility Criteria / 4.3:
Admissibility Criteria and the Type I Condition / 4.4:
Wigner Functions Associated to Nilpotent Lie Groups / 4.5:
Admissible Vectors for Group Extensions / 5:
Quasiregular Representations and the Dual Orbit Space / 5.1:
Concrete Admissibility Conditions / 5.2:
Concrete and Abstract Admissibility Conditions / 5.3:
Wavelets on Homogeneous Groups / 5.4:
Zak Transform Conditions for Weyl-Heisenberg Frames / 5.5:
Sampling Theorems for the Heisenberg Group / 6:
The Heisenberg Group and Its Lattices / 6.1:
Main Results / 6.2:
Reduction to Weyl-Heisenberg Systems / 6.3:
Weyl-Heisenberg Frames / 6.4:
Proofs of the Main Results / 6.5:
A Concrete Example / 6.6:
References
Index
Introduction / 1:
The Point of Departure / 1.1:
Overview of the Book / 1.2:
9.

図書

図書
by Han-lin Chen
出版情報: Dordrecht ; Boston : Kluwer Academic, c2000  xii, 226 p. ; 25 cm
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10.

図書

図書
Yves Meyer
出版情報: Providence, R.I. : American Mathematical Society, c1998  ix, 133 p. ; 27 cm
シリーズ名: CRM monograph series ; v. 9
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