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Record Nr. |
UNINA9911019512003321 |
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Autore |
Ruch David K. <1959-> |
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Titolo |
Wavelet theory : an elementary approach with applications / / David K. Ruch, Patrick J. Van Fleet |
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Pubbl/distr/stampa |
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Hoboken, N.J., : John Wiley & Sons, 2009 |
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ISBN |
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9786613280015 |
9781283280013 |
1283280019 |
9781118165652 |
1118165659 |
9781118165669 |
1118165667 |
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Descrizione fisica |
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1 online resource (502 p.) |
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Altri autori (Persone) |
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Van FleetPatrick J. <1962-> |
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Disciplina |
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Soggetti |
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Wavelets (Mathematics) |
Transformations (Mathematics) |
Digital images - Mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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Wavelet 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 |
3.3 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; |
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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 |
6.1 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 |
8.3 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 |
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Sommario/riassunto |
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A 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 |
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