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Mathematics for Multimedia [Hardback]

(Washington University, St. Louis)
  • Formāts: Hardback, 314 pages, height x width: 235x191 mm, weight: 720 g
  • Izdošanas datums: 07-Oct-2003
  • Izdevniecība: Academic Press Inc
  • ISBN-10: 0127484515
  • ISBN-13: 9780127484518
Citas grāmatas par šo tēmu:
  • Formāts: Hardback, 314 pages, height x width: 235x191 mm, weight: 720 g
  • Izdošanas datums: 07-Oct-2003
  • Izdevniecība: Academic Press Inc
  • ISBN-10: 0127484515
  • ISBN-13: 9780127484518
Citas grāmatas par šo tēmu:
Mathematics for Multimedia explains the mathematics behind multimedia applications such as compression, signal processing, and image/video processing. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills. More specifically, it focuses on when and why modern robust methods provide more accurate results. The topics are 'gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.

The course Mathematics for Multimedia has been offered biennially at Washington University since 1997. It has proved popular with students from sophomores to beginning graduate students who seek an innovative course of rigorous contemporary mathematics with practical applications. 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. The book also describes and illustrates easy-to-use software for applying cutting-edge techniques.

This book is aimed at a wide audience, including computer science and multimedia students and professors as well as those interested in employing mathematics in multimedia design and implementation.

Papildus informācija

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
Numbers and Arithmetic
1(23)
Integers
2(10)
Modular arithmetic
6(2)
Representing integers in binary computers
8(2)
Integer arithmetic
10(2)
Real Numbers
12(9)
Precision and accuracy
14(1)
Representing real numbers
15(3)
Propagation of error
18(3)
Exercises
21(1)
Further Reading
22(1)
Space and Linearity
23(46)
Vector Spaces
23(19)
Euclidean space
24(2)
Abstract vector spaces
26(9)
Inner product spaces
35(7)
Linear Transformations
42(23)
Matrix algebra
43(4)
Adjoints and projections
47(6)
Linear independence and invertibility
53(4)
Solving linear systems of equations
57(5)
Sparse matrices
62(3)
Exercises
65(3)
Further Reading
68(1)
Time and Frequency
69(38)
Fourier Analysis
69(25)
Periodic functions
70(2)
Localization
72(11)
Fourier series
83(11)
Discrete Fourier Analysis
94(8)
Discrete Fourier transform
95(3)
Discrete Hartley transform
98(2)
Discrete sine and cosine transforms
100(2)
Exercises
102(3)
Further Reading
105(2)
Sampling and Estimation
107(26)
Approximation and Sampling
108(15)
Polynomial interpolation
108(7)
Piecewise interpolation
115(2)
Sampling spaces
117(6)
Measurement and Estimation
123(7)
Quantization, precision, and accuracy
123(4)
Estimation
127(3)
Exercises
130(2)
Further Reading
132(1)
Scale and Resolution
133(46)
Wavelet Analysis
133(11)
Haar functions
134(2)
The affine group
136(4)
Wavelet transforms
140(4)
Discrete Wavelet Transforms
144(29)
Multiresolution analysis (MRA)
145(3)
From MRAs to filters
148(8)
From filters to discrete wavelet transforms
156(10)
Lifting
166(7)
Exercises
173(4)
Further Reading
177(2)
Redundancy and Information
179(44)
Information Source Coding
180(17)
Lossless encoding
181(5)
Efficient coding
186(5)
Huffman's algorithm
191(6)
Error Correction and Detection
197(21)
Parity bits
197(4)
Hamming codes
201(4)
Checksums and cyclic redundancy codes
205(13)
Exercises
218(2)
Further Reading
220(3)
A Answers
223(50)
...to
Chapter 1 Exercises
223(6)
...to
Chapter 2 Exercises
229(6)
...to
Chapter 3 Exercises
235(9)
...to
Chapter 4 Exercises
244(6)
...to
Chapter 5 Exercises
250(13)
...to
Chapter 6 Exercises
263(10)
B Basics, Technicalities, and Digressions
273(1)
ASCII and other character sets
273(2)
Algorithms
275(2)
Big-Oh notation
277(1)
Calculus methods
278(1)
Techniques of proof
279(1)
Limits, continuity, and derivatives
280(2)
Convergence of sequences, series and products
282(6)
Some basic probability theory
288(4)
Some more advanced results
292(2)
Rising cut-off functions
294(1)
Further Reading
295


By Mladen Victor Wickerhauser