Title Page	2
	Copyright Page	3
	Preface	6
	Table of contents	8
	List of Figures	10
	1 Introduction	12
	2 Least-squares approximation	18
	2.1 Basic notations and properties	18
	2.2 Fourier analysis	23
	2.3 Fourier transforrn	31
	3 Multiresolution	46
	3.1 Multiresolution analysis	46
	3.2 Function decomposition	50
	3.3 Pyramid algorithm	56
	3.4 Construction of rnultiresolution	58
	4 Wavelets	66
	4.1 Dilatation equation	67
	4.2 Frequency domain	70
	4.3 Matrix interpretation	74
	4.4 Properties	80
	4.5 Convergence	86
	5 How to compute	94
	5.1 Discrete wavelet transform	94
	5.2 Daubechies wavelets	104
	5.3 Biorthogonal wavelets	106
	5.4 Cardinal B-splines	109
	5.5 Interpolation wavelets	116
	5.6 Second generation wavelets	122
	5.7 Nonstandard wavelets	127
	6 Analogy with filters	134
	6.1 Signal	134
	6.2 Filter	137
	6.3 Orthogonal filter bank	142
	6.4 Daubechies filters	149
	6.5 Filter properties important for wavelets	155
	7 Applications	160
	7.1 Signal and image processing	160
	7.2 Numerical modeling	164
	Bibliography	168
	Index	172