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| Preface | ||
| Ch. 1 | Brief Historical Introduction | 1 |
| Fourier Series and Fourier Transforms | 1 | |
| Gabor Transforms | 4 | |
| The Wigner-Ville Distribution and Time-Frequency Signal Analysis | 7 | |
| Wavelet Transforms | 12 | |
| Wavelet Bases and Multiresolution Analysis | 17 | |
| Applications of Wavelet Transforms | 20 | |
| Ch. 2 | Hilbert Spaces and Orthonormal Systems | 23 |
| Normed Spaces | 25 | |
| The L[superscript p] Spaces | 28 | |
| Generalized Functions with Examples | 35 | |
| Definition and Examples of an Inner Product Space | 46 | |
| Norm in an Inner Product Space | 50 | |
| Definition and Examples of a Hilbert Space | 53 | |
| Strong and Weak Convergences | 59 | |
| Orthogonal and Orthonormal Systems | 62 | |
| Properties of Orthonormal Systems | 68 | |
| Trigonometric Fourier Series | 79 | |
| Orthogonal Complements and the Projection Theorem | 83 | |
| Linear Funtionals and the Riesz Representation Theorem | 89 | |
| Separable Hilbert Spaces | 92 | |
| Linear Operators on Hilbert Spaces | 95 | |
| Eigenvalues and Eigenvectors of an Operator | 117 | |
| Ch. 3 | Fourier Transforms and Their Applications | 143 |
| Fourier Transforms in L[superscript 1][Riemann integral] | 145 | |
| Basic Properties of Fourier Transforms | 150 | |
| Fourier Transforms in L[superscript 2][Riemann integral] | 166 | |
| Poisson's Summation Formula | 182 | |
| The Shannon Sampling Theorem and Gibbs's Phenomenon | 187 | |
| Heisenberg's Uncertainty Principle | 200 | |
| Applications of Fourier Transforms in Mathematical Statistics | 202 | |
| Applications of Fourier Transforms to Ordinary Differential Equations | 210 | |
| Solutions of Integral Equations | 214 | |
| Solutions of Partial Differential Equations | 218 | |
| Applications of Multiple Fourier Transforms to Partial Differential Equations | 230 | |
| Construction of Green's Functions by the Fourier Transform Method | 236 | |
| Ch. 4 | The Gabor Transform and Time-Frequency Signal Analysis | 257 |
| Classification of Signals and the Joint Time-Frequency Analysis of Signals | 258 | |
| Definition and Examples of the Gabor Transforms | 264 | |
| Basic Properties of Gabor Transforms | 269 | |
| Frames and Frame Operators | 274 | |
| Discrete Gabor Transforms and the Gabor Representation Problem | 284 | |
| The Zak Transform and Time-Frequency Signal Analysis | 287 | |
| Basic Properties of Zak Transforms | 290 | |
| Applications of Zak Transforms and the Balian-Low Theorem | 295 | |
| Ch. 5 | The Wigner-Ville Distribution and Time-Frequency Signal Analysis | 307 |
| Definitions and Examples of the Wigner-Ville Distribution | 308 | |
| Basic Properties of the Wigner-Ville Distribution | 319 | |
| The Wigner-Ville Distribution of Analytic Signals and Band-Limited Signals | 328 | |
| Definitions and Examples of the Woodward Ambiguity Functions | 331 | |
| Basic Properties of Ambiguity Functions | 339 | |
| The Ambiguity Transformation and Its Properties | 346 | |
| Discrete Wigner-Ville Distributions | 350 | |
| Cohen's Class of Time-Frequency Distributions | 354 | |
| Ch. 6 | Wavelet Transforms and Basic Properties | 361 |
| Continuous Wavelet Transforms and Examples | 365 | |
| Basic Properties of Wavelet Transforms | 378 | |
| The Discrete Wavelet Transforms | 382 | |
| Orthonormal Wavelets | 392 | |
| Ch. 7 | Multiresolution Analysis and Construction of Wavelets | 403 |
| Definition of Multiresolution Analysis and Examples | 405 | |
| Properties of Scaling Functions and Orthonormal Wavelet Bases | 412 | |
| Construction of Orthonormal Wavelets | 431 | |
| Daubechies' Wavelets and Algorithms | 447 | |
| Discrete Wavelet Transforms and Mallat's Pyramid Algorithm | 466 | |
| Ch. 8 | Newland's Harmonic Wavelets | 475 |
| Harmonic Wavelets | 475 | |
| Properties of Harmonic Scaling Functions | 482 | |
| Wavelet Expansions and Parseval's Formula | 485 | |
| Ch. 9 | Wavelet Transform Analysis of Turbulence | 491 |
| Fourier Transforms in Turbulence and the Navier-Stokes Equations | 495 | |
| Fractals, Multifractals, and Singularities in Turbulence | 505 | |
| Farge's Wavelet Transform Analysis of Turbulence | 512 | |
| Adaptive Wavelet Method for Analysis of Turbulent Flows | 515 | |
| Meneveau's Wavelet Analysis of Turbulence | 519 | |
| Answers and Hints for Selected Exercises | 525 | |
| Bibliography | 539 | |
| Index | 555 |
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Norman Nelsen
reviewed Wavelet Transforms And Their Applications on August 08, 2010
Wavelet Transforms And Their Applications
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Add Wavelet Transforms And Their Applications, Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms—called the fundamental building blocks at different positions and scales—and, subsequently, reconstructed with high precision. With an in, Wavelet Transforms And Their Applications to the inventory that you are selling on WonderClubX
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Add Wavelet Transforms And Their Applications, Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms—called the fundamental building blocks at different positions and scales—and, subsequently, reconstructed with high precision. With an in, Wavelet Transforms And Their Applications to your collection on WonderClub |