The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques. Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data. Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLAB?. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned. Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.
Author(s): James S. Walker
Series: Studies in Advanced Mathematics
Edition: 1
Publisher: CRC Press
Year: 1999
Language: English
Pages: 168
Tags: Приборостроение;Обработка сигналов;Вейвлет-анализ;
A Primer on Wavelets and their Scientific Applications......Page 1
Dedication......Page 2
Table of Contents......Page 3
Preface......Page 5
Acknowledgments......Page 8
1.1 The Haar transform......Page 9
Table of Contents......Page 0
Haar transform, 1-level......Page 11
Conservation of energy......Page 14
Haar transform, multiple levels......Page 16
Justification of Energy Conservation......Page 17
1.3 Haar wavelets......Page 18
1.4 Multiresolution analysis......Page 21
1.5 Compression of audio signals......Page 26
1.6 Removing noise from audio signals......Page 31
1.7 Notes and references......Page 36
2.1 The Daub4 wavelets......Page 37
Further remarks on Property I......Page 45
2.2 Conservation and compaction of energy......Page 46
Justification of conservation of energy......Page 47
How wavelet and scaling numbers are found......Page 49
2.3 Other Daubechies wavelets......Page 50
Coiflets......Page 54
2.4 Compression of audio signals......Page 57
Quantizing signal values, compressing the significance map......Page 58
2.5 Quantization, entropy, and compression......Page 61
2.6 Denoising audio signals......Page 66
Choosing a threshold value......Page 67
Removing pop noise and background static......Page 70
Discrete images......Page 73
2D wavelet transforms......Page 74
2D wavelets and scaling images......Page 77
2.8 Compression of images......Page 80
2.9 Fingerprint compression......Page 83
Remarks on the significance map......Page 85
2.10 Denoising images......Page 87
Quantitative measures of error......Page 90
Further aspects of noise removal......Page 92
Edge detection......Page 95
Edge enhancement......Page 96
Image recognition......Page 97
2.12 Notes and references......Page 100
3.1 Discrete Fourier analysis......Page 103
3.2 Definition of the DFT and its properties......Page 106
z-transforms......Page 109
3.3 Frequency description of wavelet analysis......Page 111
Low-pass and high-pass filtering......Page 114
3.4 Correlation and feature detection......Page 116
DFT method of computing correlations......Page 119
Proof of (3.40)......Page 120
Normalized correlations and feature detection......Page 121
3.5 Object detection in 2D images......Page 122
3.6 Creating scaling signals and wavelets......Page 126
3.7 Notes and references......Page 130
4.1 Wavelet packet transforms......Page 131
4.2 Applications of wavelet packet transforms......Page 134
4.3 Continuous wavelet transforms......Page 137
4.4 Gabor wavelets and speech analysis......Page 142
4.5 Notes and references......Page 146
Appendix A: Software for wavelet analysis......Page 147
Wavelet series, wavelet packet series......Page 148
Audio and image editors......Page 149
A.3 Other software......Page 150
References......Page 152
