Mathematics for Multimedia
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Table of contents
- Cover
- Contentsix
- Chapter 1. Numbers and Arithmetic1
- 1.1 Integers2
- 1.2 Real Numbers12
- 1.3 Exercises21
- 1.4 Further Reading22
- Chapter 2. Space and Linearity23
- 2.1 Vector Spaces23
- 2.2 Linear Transformations42
- 2.3 Exercises65
- 2.4 Further Reading68
- Chapter 3. Time and Frequency69
- 3.1 Fourier Analysis69
- 3.2 Discrete Fourier Analysis94
- 3.3 Exercises102
- 3.4 Further Reading105
- Chapter 4. Sampling and Estimation107
- 4.1 Approximation and Sampling108
- 4.2 Measurement and Estimation123
- 4.3 Exercises130
- 4.4 Further Reading132
- Chapter 5. Scale and Resolution133
- 5.1 Wavelet Analysis133
- 5.2 Discrete Wavelet Transforms144
- 5.3 Exercises173
- 5.4 Further Reading177
- Chapter 6. Redundancy and Information179
- 6.1 Information Source Coding180
- 6.2 Error Correction and Detection197
- 6.3 Exercises218
- 6.4 Further Reading220
- Appendix A. Answers223
- A.1 to Chapter 1 Exercises223
- A.2 to Chapter 2 Exercises229
- A.3 to Chapter 3 Exercises235
- A.4 to Chapter 4 Exercises244
- A.5 to Chapter 5 Exercises250
- A.6 t o Chapter 6 Exercises263
- Appendix B. Basics, Technicalities, and Digressions273
- B.1 ASCII and other character sets273
- B.2 Algorithms275
- B.3 Big-Oh notation277
- B.4 Calculus methods278
- B.5 Some basic probability theory288
- B.6 Some more advanced results292
- B.7 Rising cut-off functions294
- B.8 Further Reading295
- Index297
Mathematics and Multimedia focuses on the mathematics behind multimedia applications. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills.The topics are `gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.The book is aimed at a wide audience, including computer science and mathematics majors and those interested in employing mathematics in multimedia design and implementation.
For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and students on challenging equations, and their solutions.
Explains when and why modern robust methods provide more accurate results
Does not assume or require previous training in statistics
Includes many illustrations using data from actual studies
Describes and illustrates easy-to-use software for applying cutting-edge techniques
For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and students on challenging equations, and their solutions.
Explains when and why modern robust methods provide more accurate results
Does not assume or require previous training in statistics
Includes many illustrations using data from actual studies
Describes and illustrates easy-to-use software for applying cutting-edge techniques