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Mathematics for Multimedia / by Mladen Victor Wickerhauser
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Applied and Numerical Harmonic Analysis | SpringerLink BücherPublisher: Boston : Birkhäuser Boston, 2010Edition: 1Description: Online-Ressource (XVII, 305p. 37 illus, digital)ISBN:- 9780817648800
- 519
- 515.2433 23
- 006.760151
- T57-57.97
- QA39.3
Contents:
Summary: Numbers and Arithmetic -- Space and Linearity -- Time and Frequency -- Sampling and Estimation -- Scale and Resolution -- Redundancy and Information -- Answers -- Basics, Technicalities, and Digressions.Summary: This concise textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebra and analysis, the work examines tools used to create application software for multimedia signal processing and communication. Key features include: * Over 100 exercises with complete solutions; * Useful algorithms presented in pseudocode and Standard C to help readers with programming, experimentation, and the solution of exercises; * Numerous illustrations based on data from real studies; * Suggestions for further reading at the end of each chapter; * A companion website—maintained by the author—providing computer programs described in the book as well as additional references and data files, such as images and sounds, to enhance the reader’s understanding of key topics; * A supplementary manual—containing several hundred exercises, solutions, and sample programs not included in the book—available to instructors upon request; * Minimal prerequisites—only an undergraduate-level knowledge of mathematics, not including statistics, is required. Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in pure and applied mathematics, engineering, and computer science seeking an innovative approach to contemporary mathematics with practical applications. The work may also serve as a useful reference for multimedia applications developers and other researchers and practitioners interested in the mathematics underlying multimedia software design and implementation.PPN: PPN: 1649896298Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""ANHA Series Preface""; ""Preface""; ""How to Use This Book""; ""Contents""; ""Numbers and Arithmetic""; ""1.1 Integers""; ""1.1.1 Modular arithmetic""; ""1.1.2 Representing integers in binary computers""; ""1.1.3 Integer arithmetic""; ""1.2 Real Numbers""; ""1.2.1 Precision and accuracy""; ""1.2.2 Representing real numbers""; ""1.2.3 Propagation of error""; ""1.3 Exercises""; ""1.4 Further Reading""; ""Space and Linearity""; ""2.1 Vector Spaces""; ""2.1.1 Euclidean space""; ""2.1.2 Abstract vector spaces""; ""2.1.3 Inner product spaces""; ""2.2 Linear Transformations""
""2.2.1 Matrix algebra""""2.2.2 Adjoints and projections""; ""2.2.3 Linear independence and invertibility""; ""2.2.4 Solving linear systems of equations""; ""2.2.5 Sparse matrices""; ""2.3 Exercises""; ""2.4 Further Reading""; ""Time and Frequency""; ""3.1 Fourier Analysis""; ""3.1.1 Periodic functions""; ""3.1.2 Localization""; ""3.1.3 Fourier series""; ""3.2 Discrete Fourier Analysis""; ""3.2.1 Discrete Fourier transform""; ""3.2.2 Discrete Hartley transform""; ""3.2.3 Discrete sine and cosine transforms""; ""3.3 Exercises""; ""3.4 Further Reading""; ""Sampling and Estimation""
""4.1 Approximation and Sampling""""4.1.1 Polynomial interpolation""; ""4.1.2 Piecewise interpolation""; ""4.1.3 Sampling spaces""; ""4.2 Measurement and Estimation""; ""4.2.1 Quantization, precision, and accuracy""; ""4.2.2 Estimation""; ""4.3 Exercises""; ""4.4 Further Reading""; ""Scale and Resolution""; ""5.1 Wavelet Analysis""; ""5.1.1 Haar functions""; ""5.1.2 The affine group""; ""5.1.3 Wavelet transforms""; ""5.2 Discrete Wavelet Transforms""; ""5.2.1 Multiresolution analysis (MRA)""; ""5.2.2 From MRAs to filters""; ""5.2.3 From filters to discrete wavelet transforms""
""5.2.4 Lifting""""5.3 Exercises""; ""5.4 Further Reading""; ""Redundancy and Information""; ""6.1 Information Source Coding""; ""6.1.1 Lossless encoding""; ""6.1.2 Efficient coding""; ""6.1.3 Huffman�s algorithm""; ""6.2 Error Correction and Detection""; ""6.2.1 Parity bits""; ""6.2.2 Hamming codes""; ""6.2.3 Checksums and cyclic redundancy codes""; ""6.3 Exercises""; ""6.4 Further Reading""; ""Answers""; ""A.1 . . . to Chapter 1 Exercises""; ""A.2 . . . to Chapter 2 Exercises""; ""A.3 . . . to Chapter 3 Exercises""; ""A.4 . . . to Chapter 4 Exercises""
""A.5 . . . to Chapter 5 Exercises""""A.6 . . . to Chapter 6 Exercises""; ""Basics, Technicalities, andDigressions""; ""B.1 ASCII and other character sets""; ""B.2 Algorithms""; ""B.3 Big-Oh notation""; ""B.4 Calculus methods""; ""B.4.1 Techniques of proof""; ""B.4.2 Limits, continuity, and derivatives""; ""B.4.3 Convergence of sequences, series and products""; ""B.5 Some basic probability theory""; ""B.6 Some more advanced results""; ""B.7 Rising cut-off functions""; ""B.8 Further Reading""; ""Index""
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