LEADER 04597nam 2200613 a 450 001 9910830325103321 005 20230721010637.0 010 $a1-283-28001-9 010 $a9786613280015 010 $a1-118-16565-9 010 $a1-118-16566-7 035 $a(CKB)2550000000052805 035 $a(EBL)818929 035 $a(OCoLC)757511735 035 $a(SSID)ssj0000542481 035 $a(PQKBManifestationID)11322900 035 $a(PQKBTitleCode)TC0000542481 035 $a(PQKBWorkID)10510007 035 $a(PQKB)11539528 035 $a(MiAaPQ)EBC818929 035 $a(EXLCZ)992550000000052805 100 $a20090429d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aWavelet theory$b[electronic resource] $ean elementary approach with applications /$fDavid K. Ruch, Patrick J. Van Fleet 210 $aHoboken, N.J. $cJohn Wiley & Sons$d2009 215 $a1 online resource (502 p.) 300 $aDescription based upon print version of record. 311 $a0-470-38840-4 320 $aIncludes bibliographical references and indexes. 327 $aWavelet Theory: An Elementary Approach with Applications; CONTENTS; Preface; Acknowledgments; 1 The Complex Plane and the Space L2(R); 1.1 Complex Numbers and Basic Operations; Problems; 1.2 The Space L2(R); Problems; 1.3 Inner Products; Problems; 1.4 Bases and Projections; Problems; 2 Fourier Series and Fourier Transformations; 2.1 Euler's Formula and the Complex Exponential Function; Problems; 2.2 Fourier Series; Problems; 2.3 The Fourier Transform; Problems; 2.4 Convolution and 5-Splines; Problems; 3 Haar Spaces; 3.1 The Haar Space Vo; Problems; 3.2 The General Haar Space Vj; Problems 327 $a3.3 The Haar Wavelet Space W0Problems; 3.4 The General Haar Wavelet Space Wj; Problems; 3.5 Decomposition and Reconstruction; Problems; 3.6 Summary; 4 The Discrete Haar Wavelet Transform and Applications; 4.1 The One-Dimensional Transform; Problems; 4.2 The Two-Dimensional Transform; Problems; 4.3 Edge Detection and Naive Image Compression; 5 Multiresolution Analysis; 5.1 Multiresolution Analysis; Problems; 5.2 The View from the Transform Domain; Problems; 5.3 Examples of Multiresolution Analyses; Problems; 5.4 Summary; 6 Daubechies Scaling Functions and Wavelets 327 $a6.1 Constructing the Daubechies Scaling FunctionsProblems; 6.2 The Cascade Algorithm; Problems; 6.3 Orthogonal Translates, Coding, and Projections; Problems; 7 The Discrete Daubechies Transformation and Applications; 7.1 The Discrete Daubechies Wavelet Transform; Problems; 7.2 Projections and Signal and Image Compression; Problems; 7.3 Naive Image Segmentation; Problems; 8 Biorthogonal Scaling Functions and Wavelets; 8.1 A Biorthogonal Example and Duality; Problems; 8.2 Biorthogonality Conditions for Symbols and Wavelet Spaces; Problems 327 $a8.3 Biorthogonal Spline Filter Pairs and the CDF97 Filter PairProblems; 8.4 Decomposition and Reconstruction; Problems; 8.5 The Discrete Biorthogonal Wavelet Transform; Problems; 8.6 Riesz Basis Theory; Problems; 9 Wavelet Packets; 9.1 Constructing Wavelet Packet Functions; Problems; 9.2 Wavelet Packet Spaces; Problems; 9.3 The Discrete Packet Transform and Best Basis Algorithm; Problems; 9.4 The FBI Fingerprint Compression Standard; Appendix A: Huffman Coding; Problems; References; Topic Index; Author Index 330 $aA self-contained, elementary introduction to wavelet theory and applications Exploring 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. The book begins with a brief introduction to the fundamentals of com 606 $aWavelets (Mathematics) 606 $aTransformations (Mathematics) 606 $aDigital images$xMathematics 615 0$aWavelets (Mathematics) 615 0$aTransformations (Mathematics) 615 0$aDigital images$xMathematics. 676 $a515.2433 700 $aRuch$b David K.$f1959-$01696399 701 $aVan Fleet$b Patrick J.$f1962-$0521988 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830325103321 996 $aWavelet theory$94076357 997 $aUNINA