Mathematics for Multimedia

by Wickerhauser

• ISBN13: 9780127484518
• ISBN10: 0127484515
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-09-09
• Publisher: Elsevier Science

Summary

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.

Table of Contents

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