{"product_id":"wavelet-theory-9780470388402","title":"Wavelet Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA self-contained, elementary introduction to wavelet theory and applications  \u003cp\u003eExploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications.\u003c\/p\u003e \u003cp\u003eThe book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets,\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The book, putting emphasize on an analytic facet of wavelets, can be seen as complementary\u003cbr\u003e to the previous Patrick J. Van Fleet's book, DiscreteWavelet Transformations: An Elementary\u003cbr\u003e Approach with Applications, focused on their algebraic properties.\" (Zentralblatt MATH, 2011)  \u003c\/p\u003e\u003cp\u003e\"Requiring only a prerequisite knowledge of calculus and linear algebra, Wavelet theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level.\" (Mathematical Reviews, 2011)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e²Preface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The Complex Plane and the Space L²(R) 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Complex Numbers and Basic Operations 1\u003c\/p\u003e \u003cp\u003eProblems 5\u003c\/p\u003e \u003cp\u003e1.2 The Space L²(R) 7\u003c\/p\u003e \u003cp\u003eProblems 16\u003c\/p\u003e \u003cp\u003e1.3 Inner Products 18\u003c\/p\u003e \u003cp\u003eProblems 25\u003c\/p\u003e \u003cp\u003e1.4 Bases and Projections 26\u003c\/p\u003e \u003cp\u003eProblems 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fourier Series and Fourier Transformations 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Euler's Formula and the Complex Exponential Function 32\u003c\/p\u003e \u003cp\u003eProblems 36\u003c\/p\u003e \u003cp\u003e2.2 Fourier Series 37\u003c\/p\u003e \u003cp\u003eProblems 49\u003c\/p\u003e \u003cp\u003e2.3 The Fourier Transform 53\u003c\/p\u003e \u003cp\u003eProblems 66\u003c\/p\u003e \u003cp\u003e2.4 Convolution and 5-Splines 72\u003c\/p\u003e \u003cp\u003eProblems 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Haar Spaces 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Haar Space Vo 86\u003c\/p\u003e \u003cp\u003eProblems 93\u003c\/p\u003e \u003cp\u003e3.2 The General Haar Space Vj 93\u003c\/p\u003e \u003cp\u003eProblems 107\u003c\/p\u003e \u003cp\u003e3.3 The Haar Wavelet Space W0 108\u003c\/p\u003e \u003cp\u003eProblems 119\u003c\/p\u003e \u003cp\u003e3.4 The General Haar Wavelet Space Wj 120\u003c\/p\u003e \u003cp\u003eProblems 133\u003c\/p\u003e \u003cp\u003e3.5 Decomposition and Reconstruction 134\u003c\/p\u003e \u003cp\u003eProblems 140\u003c\/p\u003e \u003cp\u003e3.6 Summary 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Discrete Haar Wavelet Transform and Applications 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The One-Dimensional Transform 146\u003c\/p\u003e \u003cp\u003eProblems 159\u003c\/p\u003e \u003cp\u003e4.2 The Two-Dimensional Transform 163\u003c\/p\u003e \u003cp\u003eProblems 171\u003c\/p\u003e \u003cp\u003e4.3 Edge Detection and Naive Image Compression 172\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Multiresolution Analysis 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Multiresolution Analysis 180\u003c\/p\u003e \u003cp\u003eProblems 196\u003c\/p\u003e \u003cp\u003e5.2 The View from the Transform Domain 200\u003c\/p\u003e \u003cp\u003eProblems 212\u003c\/p\u003e \u003cp\u003e5.3 Examples of Multiresolution Analyses 216\u003c\/p\u003e \u003cp\u003eProblems 224\u003c\/p\u003e \u003cp\u003e5.4 Summary 225\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Daubechies Scaling Functions and Wavelets 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Constructing the Daubechies Scaling Functions 234\u003c\/p\u003e \u003cp\u003eProblems 246\u003c\/p\u003e \u003cp\u003e6.2 The Cascade Algorithm 251\u003c\/p\u003e \u003cp\u003eProblems 265\u003c\/p\u003e \u003cp\u003e6.3 Orthogonal Translates, Coding, and Projections 268\u003c\/p\u003e \u003cp\u003eProblems 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 The Discrete Daubechies Transformation and Applications 277\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Discrete Daubechies Wavelet Transform 278\u003c\/p\u003e \u003cp\u003eProblems 290\u003c\/p\u003e \u003cp\u003e7.2 Projections and Signal and Image Compression 293\u003c\/p\u003e \u003cp\u003eProblems 310\u003c\/p\u003e \u003cp\u003e7.3 Naive Image Segmentation 314\u003c\/p\u003e \u003cp\u003eProblems 322\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Biorthogonal Scaling Functions and Wavelets 325\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 A Biorthogonal Example and Duality 326\u003c\/p\u003e \u003cp\u003eProblems 333\u003c\/p\u003e \u003cp\u003e8.2 Biorthogonality Conditions for Symbols and Wavelet Spaces 334\u003c\/p\u003e \u003cp\u003eProblems 350\u003c\/p\u003e \u003cp\u003e8.3 Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair 353\u003c\/p\u003e \u003cp\u003eProblems 368\u003c\/p\u003e \u003cp\u003e8.4 Decomposition and Reconstruction 370\u003c\/p\u003e \u003cp\u003eProblems 375\u003c\/p\u003e \u003cp\u003e8.5 The Discrete Biorthogonal Wavelet Transform 375\u003c\/p\u003e \u003cp\u003eProblems 388\u003c\/p\u003e \u003cp\u003e8.6 Riesz Basis Theory 390\u003c\/p\u003e \u003cp\u003eProblems 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Wavelet Packets 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Constructing Wavelet Packet Functions 400\u003c\/p\u003e \u003cp\u003eProblems 413\u003c\/p\u003e \u003cp\u003e9.2 Wavelet Packet Spaces 414\u003c\/p\u003e \u003cp\u003eProblems 424\u003c\/p\u003e \u003cp\u003e9.3 The Discrete Packet Transform and Best Basis Algorithm 424\u003c\/p\u003e \u003cp\u003eProblems 439\u003c\/p\u003e \u003cp\u003e9.4 The FBI Fingerprint Compression Standard 440\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Huffman Coding 455\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eProblems 462\u003c\/p\u003e \u003cp\u003eReferences 465\u003c\/p\u003e \u003cp\u003eTopic Index 469\u003c\/p\u003e \u003cp\u003eAuthor Index 479\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402320748887,"sku":"9780470388402","price":99.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470388402.jpg?v=1730480062","url":"https:\/\/bookcurl.com\/products\/wavelet-theory-9780470388402","provider":"Book Curl","version":"1.0","type":"link"}