Elements of wavelets for engineers and scientists

Title:

Personal Author:

Mix, Dwight F., 1932-

Publication Information:

Hoboken, N.J. : Wiley-Interscience, 2003

ISBN:

9780471466178

Subject Term:

Wavelets (Mathematics)

Engineering mathematics

Added Author:

Olejniczak, Kraig J.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010045580	QA403.3 M59 2003	Open Access Book	Book	Searching... Unknown

An indispensable guide to understanding wavelets
Elements of Wavelets for Engineers and Scientists is a guide to wavelets for "the rest of us"-practicing engineers and scientists, nonmathematicians who want to understand and apply such tools as fast Fourier and wavelet transforms. It is carefully designed to help professionals in nonmathematical fields comprehend this very mathematically sophisticated topic and be prepared for further study on a more mathematically rigorous level.
Detailed discussions, worked-out examples, drawings, and drill problems provide step-by-step guidance on fundamental concepts such as vector spaces, metric, norm, inner product, basis, dimension, biorthogonality, and matrices.
Chapters explore . . .
* Functions and transforms
* The sampling theorem
* Multirate processing
* The fast Fourier transform
* The wavelet transform
* QMF filters
* Practical wavelets and filters
. . . as well as many new wavelet applications-image compression, turbulence, and pattern recognition, for instance-that have resulted from recent synergies in fields such as quantum physics and seismic geology.
Elements of Wavelets for Engineers and Scientists is a must for every practicing engineer, scientist, computer programmer, and student needing a practical, top-to-bottom grasp of wavelets.

Author Notes

DWIGHT F. MIX, PhD, PE, is Professor Emeritus at the University of Arkansas, where he taught from 1965 to 1998 in the Department of Electrical Engineering.
Kraig J. Olejniczak, PhD, PE, is Dean of the College of Engineering at Valparaiso University. He served on the faculty of the University of Arkansas Department of Electrical Energy from 1991 to 2002.

Preface	p. vii
1. Functions and Transforms	p. 1
1.1. Wavelet Transform	p. 1
1.2. Transforms	p. 5
1.3. Power and Energy Signals	p. 9
1.4. Deterministic and Random Signals	p. 16
1.5. Fourier and Haar Transforms	p. 18
2. Vectors	p. 25
2.1. Vector Space	p. 26
2.2. Metric Space	p. 31
2.3. Norm	p. 36
2.4. Inner Product	p. 39
2.5. Orthogonality	p. 45
3. Basis and Dimension	p. 47
3.1. Linear Independence	p. 48
3.2. Basis	p. 51
3.3. Dimension and Span	p. 54
3.4. Reciprocal Bases	p. 56
4. Linear Transformations	p. 65
4.1. Component Vectors	p. 65
4.2. Matrices	p. 69
5. Sampling Theorem	p. 80
5.1. Nyquist Rate	p. 80
5.2. Nonperiodic Sampling	p. 88
5.3. Quantization and Pulse Code Modulation	p. 90
5.4. Companding	p. 93
6. Multirate Processing	p. 95
6.1. Downsampling	p. 95
6.2. Upsampling	p. 103
6.3. Fractional Rate Change	p. 104
6.4. Downsampling and Correlation	p. 110
6.5. Upsampling and Convolution	p. 116
7. Fast Fourier Transform	p. 121
7.1. Discrete-Time Fourier Series	p. 121
7.2. Matrix Decomposition View	p. 125
7.3. Signal Flow Graph Representation	p. 128
7.4. Downsampling View	p. 139
8. Wavelet Transform	p. 145
8.1. Scaling Functions and Wavelets	p. 145
8.2. Discrete Wavelet Transform	p. 162
9. Quadrature Mirror Filters	p. 170
9.1. Allpass Networks	p. 170
9.2. Quadrature Mirror Filters	p. 181
9.3. Filter Banks	p. 186
10. Practical Wavelets and Filters	p. 195
10.1. Practical Wavelets	p. 195
10.2. The Magic Part	p. 201
10.3. Other Wavelets	p. 208
10.4. Matrix of Transformation	p. 213
11. Using Wavelets	p. 219
11.1. Top-Down Approach	p. 219
11.2. Pattern Recognition	p. 227
11.3. Hidden Singularities	p. 230
11.4. Data Compression	p. 232
Index	p. 235

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Author Notes

Table of Contents