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E-grāmata: Mathematics for Multimedia

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This 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 * Many sample programs in Standard C* Numerous illustrations based on data from real studies* Suggestions for further reading at the end of each chapter* A companion website providing the 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* Only undergraduate-level knowledge of mathematics and no previous knowledge of statistics are requiredMathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to rigorous, contemporary mathematics with practical applications. The work may also serve as an invaluable reference for multimedia applications developers and all those interested in the mathematics underlying multimedia design and implementation.

This 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. Replete with exercises, sample programs in Standard C, and numerous illustrations, Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to contemporary mathematics with practical applications. The work may also serve as an invaluable reference for multimedia applications developers and all those interested in the mathematics underlying multimedia design and implementation.

Recenzijas

From the reviews:

The book under review is aimed at providing a comprehensive understanding to undergraduate students who have got beyond Calculus. Students in mathematics, computer science and engineering will benefit from the material and mathematical concepts presented in this book. (Carnelia Bejan, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)

This concise textbook on applied Fourier analysis presents the mathematics that is fundamental to applications in digital signal processing. The main emphasis of the author is on practical implementation of algorithms in multimedia applications. Key algorithms are presented in pseudocode and Standard C. This well-written textbook on applied Fourier analysis is very convenient for students in applied mathematics and computer science. This book can also serve as useful reference for researchers interested in the mathematics underlying multimedia software design and implementation. (Manfred Tasche, Zentralblatt MATH, Vol. 1183, 2010)

"Aside from introductory material in the first two chapters, chapters are independent, which means that the instructor can tailor the material as needed. The text contains a number of fascinating and beautiful results; having never studied Fourier series or coding theory before, I found myself smiling in admiration at a few of them, and made notes about a couple. The text is clear and develops carefully. Exercises range from easy to challenging, and complete (!) solutions appear in an appendix."

MAA Reviews

ANHA Series Preface vii
Preface xi
How to Use This Book xii
Numbers and Arithmetic
1(22)
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)
Chapter 1 Exercises
223(6)
Chapter 2 Exercises
229(6)
Chapter 3 Exercises
235(9)
Chapter 4 Exercises
244(6)
Chapter 5 Exercises
250(13)
Chapter 6 Exercises
263(10)
B Basics, Technicalities, and Digressions
273(24)
ASCII and other character sets
273(2)
Algorithms
275(2)
Big-Oh notation
277(1)
Calculus methods
278(10)
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(2)
Index 297