{"product_id":"a-first-course-in-wavelets-with-fourier-analysis-9780470431177","title":"A First Course in Wavelets with Fourier Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eA comprehensive, self-contained treatment of Fourier analysis and waveletsnow in a new edition\u003c\/b\u003e  \u003cp\u003eThrough expansive coverage and easy-to-follow explanations, A \u003ci\u003eFirst Course in Wavelets with Fourier Analysis\u003c\/i\u003e, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level.\u003c\/p\u003e \u003cp\u003eThe book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe development of a Fourier series, Fourier transform, and discrete Fourier analysis\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eImproved sections devoted to continuous wavelets and two-dimensional wavelets\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe analysis of Haar, Shannon, and line\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"A first course in wavelets with Fourier analysis, second edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.\" (Mathematical Reviews, 2011)\u003cbr\u003e \u003cbr\u003e   \u003c\/p\u003e\n\u003cp\u003e\"The discussions of applications avoid the deep jargon of signal processing … accessible to a wider audience.\" (\u003ci\u003eBook News\u003c\/i\u003e, December 2009)\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface and Overview ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e0 Inner Product Spaces 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e0.1 Motivation, 1\u003c\/p\u003e \u003cp\u003e0.2 Definition of Inner Product, 2\u003c\/p\u003e \u003cp\u003e0.3 The Spaces L2 and l2, 4\u003c\/p\u003e \u003cp\u003e0.3.1 Definitions, 4\u003c\/p\u003e \u003cp\u003e0.3.2 Convergence in L2 Versus Uniform Convergence, 8\u003c\/p\u003e \u003cp\u003e0.4 Schwarz and Triangle Inequalities, 11\u003c\/p\u003e \u003cp\u003e0.5 Orthogonality, 13\u003c\/p\u003e \u003cp\u003e0.5.1 Definitions and Examples, 13\u003c\/p\u003e \u003cp\u003e0.5.2 Orthogonal Projections, 15\u003c\/p\u003e \u003cp\u003e0.5.3 Gram–Schmidt Orthogonalization, 20\u003c\/p\u003e \u003cp\u003e0.6 Linear Operators and Their Adjoints, 21\u003c\/p\u003e \u003cp\u003e0.6.1 Linear Operators, 21\u003c\/p\u003e \u003cp\u003e0.6.2 Adjoints, 23\u003c\/p\u003e \u003cp\u003e0.7 Least Squares and Linear Predictive Coding, 25\u003c\/p\u003e \u003cp\u003e0.7.1 Best-Fit Line for Data, 25\u003c\/p\u003e \u003cp\u003e0.7.2 General Least Squares Algorithm, 29\u003c\/p\u003e \u003cp\u003e0.7.3 Linear Predictive Coding, 31\u003c\/p\u003e \u003cp\u003eExercises, 34\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Fourier Series 38\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction, 38\u003c\/p\u003e \u003cp\u003e1.1.1 Historical Perspective, 38\u003c\/p\u003e \u003cp\u003e1.1.2 Signal Analysis, 39\u003c\/p\u003e \u003cp\u003e1.1.3 Partial Differential Equations, 40\u003c\/p\u003e \u003cp\u003e1.2 Computation of Fourier Series, 42\u003c\/p\u003e \u003cp\u003e1.2.1 On the Interval −π ≤ x ≤ π, 42\u003c\/p\u003e \u003cp\u003e1.2.2 Other Intervals, 44\u003c\/p\u003e \u003cp\u003e1.2.3 Cosine and Sine Expansions, 47\u003c\/p\u003e \u003cp\u003e1.2.4 Examples, 50\u003c\/p\u003e \u003cp\u003e1.2.5 The Complex Form of Fourier Series, 58\u003c\/p\u003e \u003cp\u003e1.3 Convergence Theorems for Fourier Series, 62\u003c\/p\u003e \u003cp\u003e1.3.1 The Riemann–Lebesgue Lemma, 62\u003c\/p\u003e \u003cp\u003e1.3.2 Convergence at a Point of Continuity, 64\u003c\/p\u003e \u003cp\u003e1.3.3 Convergence at a Point of Discontinuity, 69\u003c\/p\u003e \u003cp\u003e1.3.4 Uniform Convergence, 72\u003c\/p\u003e \u003cp\u003e1.3.5 Convergence in the Mean, 76\u003c\/p\u003e \u003cp\u003eExercises, 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Fourier Transform 92\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Informal Development of the Fourier Transform, 92\u003c\/p\u003e \u003cp\u003e2.1.1 The Fourier Inversion Theorem, 92\u003c\/p\u003e \u003cp\u003e2.1.2 Examples, 95\u003c\/p\u003e \u003cp\u003e2.2 Properties of the Fourier Transform, 101\u003c\/p\u003e \u003cp\u003e2.2.1 Basic Properties, 101\u003c\/p\u003e \u003cp\u003e2.2.2 Fourier Transform of a Convolution, 107\u003c\/p\u003e \u003cp\u003e2.2.3 Adjoint of the Fourier Transform, 109\u003c\/p\u003e \u003cp\u003e2.2.4 Plancherel Theorem, 109\u003c\/p\u003e \u003cp\u003e2.3 Linear Filters, 110\u003c\/p\u003e \u003cp\u003e2.3.1 Time-Invariant Filters, 110\u003c\/p\u003e \u003cp\u003e2.3.2 Causality and the Design of Filters, 115\u003c\/p\u003e \u003cp\u003e2.4 The Sampling Theorem, 120\u003c\/p\u003e \u003cp\u003e2.5 The Uncertainty Principle, 123\u003c\/p\u003e \u003cp\u003eExercises, 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Discrete Fourier Analysis 132\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Discrete Fourier Transform, 132\u003c\/p\u003e \u003cp\u003e3.1.1 Definition of Discrete Fourier Transform, 134\u003c\/p\u003e \u003cp\u003e3.1.2 Properties of the Discrete Fourier Transform, 135\u003c\/p\u003e \u003cp\u003e3.1.3 The Fast Fourier Transform, 138\u003c\/p\u003e \u003cp\u003e3.1.4 The FFT Approximation to the Fourier Transform, 143\u003c\/p\u003e \u003cp\u003e3.1.5 Application: Parameter Identification, 144\u003c\/p\u003e \u003cp\u003e3.1.6 Application: Discretizations of Ordinary Differential Equations, 146\u003c\/p\u003e \u003cp\u003e3.2 Discrete Signals, 147\u003c\/p\u003e \u003cp\u003e3.2.1 Time-Invariant, Discrete Linear Filters, 147\u003c\/p\u003e \u003cp\u003e3.2.2 Z-Transform and Transfer Functions, 149\u003c\/p\u003e \u003cp\u003e3.3 Discrete Signals \u0026amp; Matlab, 153\u003c\/p\u003e \u003cp\u003eExercises, 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Haar Wavelet Analysis 160\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Why Wavelets?, 160\u003c\/p\u003e \u003cp\u003e4.2 Haar Wavelets, 161\u003c\/p\u003e \u003cp\u003e4.2.1 The Haar Scaling Function, 161\u003c\/p\u003e \u003cp\u003e4.2.2 Basic Properties of the Haar Scaling Function, 167\u003c\/p\u003e \u003cp\u003e4.2.3 The Haar Wavelet, 168\u003c\/p\u003e \u003cp\u003e4.3 Haar Decomposition and Reconstruction Algorithms, 172\u003c\/p\u003e \u003cp\u003e4.3.1 Decomposition, 172\u003c\/p\u003e \u003cp\u003e4.3.2 Reconstruction, 176\u003c\/p\u003e \u003cp\u003e4.3.3 Filters and Diagrams, 182\u003c\/p\u003e \u003cp\u003e4.4 Summary, 185\u003c\/p\u003e \u003cp\u003eExercises, 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Multiresolution Analysis 190\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Multiresolution Framework, 190\u003c\/p\u003e \u003cp\u003e5.1.1 Definition, 190\u003c\/p\u003e \u003cp\u003e5.1.2 The Scaling Relation, 194\u003c\/p\u003e \u003cp\u003e5.1.3 The Associated Wavelet and Wavelet Spaces, 197\u003c\/p\u003e \u003cp\u003e5.1.4 Decomposition and Reconstruction Formulas: A Tale of Two Bases, 201\u003c\/p\u003e \u003cp\u003e5.1.5 Summary, 203\u003c\/p\u003e \u003cp\u003e5.2 Implementing Decomposition and Reconstruction, 204\u003c\/p\u003e \u003cp\u003e5.2.1 The Decomposition Algorithm, 204\u003c\/p\u003e \u003cp\u003e5.2.2 The Reconstruction Algorithm, 209\u003c\/p\u003e \u003cp\u003e5.2.3 Processing a Signal, 213\u003c\/p\u003e \u003cp\u003e5.3 Fourier Transform Criteria, 214\u003c\/p\u003e \u003cp\u003e5.3.1 The Scaling Function, 215\u003c\/p\u003e \u003cp\u003e5.3.2 Orthogonality via the Fourier Transform, 217\u003c\/p\u003e \u003cp\u003e5.3.3 The Scaling Equation via the Fourier Transform, 221\u003c\/p\u003e \u003cp\u003e5.3.4 Iterative Procedure for Constructing the Scaling Function, 225\u003c\/p\u003e \u003cp\u003eExercises, 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Daubechies Wavelets 234\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Daubechies’ Construction, 234\u003c\/p\u003e \u003cp\u003e6.2 Classification, Moments, and Smoothness, 238\u003c\/p\u003e \u003cp\u003e6.3 Computational Issues, 242\u003c\/p\u003e \u003cp\u003e6.4 The Scaling Function at Dyadic Points, 244\u003c\/p\u003e \u003cp\u003eExercises, 248\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Other Wavelet Topics 250\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Computational Complexity, 250\u003c\/p\u003e \u003cp\u003e7.1.1 Wavelet Algorithm, 250\u003c\/p\u003e \u003cp\u003e7.1.2 Wavelet Packets, 251\u003c\/p\u003e \u003cp\u003e7.2 Wavelets in Higher Dimensions, 253\u003c\/p\u003e \u003cp\u003eExercises on 2D Wavelets, 258\u003c\/p\u003e \u003cp\u003e7.3 Relating Decomposition and Reconstruction, 259\u003c\/p\u003e \u003cp\u003e7.3.1 Transfer Function Interpretation, 263\u003c\/p\u003e \u003cp\u003e7.4 Wavelet Transform, 266\u003c\/p\u003e \u003cp\u003e7.4.1 Definition of the Wavelet Transform, 266\u003c\/p\u003e \u003cp\u003e7.4.2 Inversion Formula for the Wavelet Transform, 268\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Technical Matters 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Proof of the Fourier Inversion Formula, 273\u003c\/p\u003e \u003cp\u003eA.2 Technical Proofs from Chapter 5, 277\u003c\/p\u003e \u003cp\u003eA.2.1 Rigorous Proof of Theorem 5.17, 277\u003c\/p\u003e \u003cp\u003eA.2.2 Proof of Theorem 5.10, 281\u003c\/p\u003e \u003cp\u003eA.2.3 Proof of the Convergence Part of Theorem 5.23, 283\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B: Solutions to Selected Exercises 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C: MATLAB® Routines 305\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 General Compression Routine, 305\u003c\/p\u003e \u003cp\u003eC.2 Use of MATLAB’s FFT Routine for Filtering and Compression, 306\u003c\/p\u003e \u003cp\u003eC.3 Sample Routines Using MATLAB’s Wavelet Toolbox, 307\u003c\/p\u003e \u003cp\u003eC.4 MATLAB Code for the Algorithms in Section 5.2, 308\u003c\/p\u003e \u003cp\u003eBibliography 311\u003c\/p\u003e \u003cp\u003eIndex 313\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402331496791,"sku":"9780470431177","price":97.16,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/a-first-course-in-wavelets-with-fourier-analysis-9780470431177","provider":"Book Curl","version":"1.0","type":"link"}