A Primer on Wavelets and Their Scientific Applications Book

1	Haar Wavelets	1
1.1	The Haar transform	1
1.2	Conservation and compaction of energy	6
1.3	Haar wavelets	10
1.4	Multiresolution analysis	13
1.5	Compression of audio signals	18
1.6	Removing noise from audio signals	23
1.7	Notes and references	28
2	Daubechies wavelets	29
2.1	The Daub4 wavelets	29
2.2	Conservation and compaction of energy	38
2.3	Other Daubechies wavelets	42
2.4	Compression of audio signals	49
2.5	Quantization, entropy, and compression	53
2.6	Denoising audio signals	58
2.7	Two-dimensional wavelet transforms	65
2.8	Compression of images	72
2.9	Fingerprint compression	75
2.10	Denoising images	79
2.11	Some topics in image processing	87
2.12	Notes and references	92
3	Frequency analysis	95
3.1	Discrete Fourier analysis	95
3.2	Definition of the DFT and its properties	98
3.3	Frequency description of wavelet analysis	103
3.4	Correlation and feature detection	108
3.5	Object detection in 2D images	114
3.6	Creating scaling signals and wavelets	118
3.7	Notes and references	122
4	Beyond wavelets	123
4.1	Wavelet packet transforms	123
4.2	Applications of wavelet packet transforms	126
4.3	Continuous wavelet transforms	129
4.4	Gabor wavelets and speech analysis	134
4.5	Notes and references	138
A	Software for wavelet analysis	139
	References	145
	Index	151