书籍介绍

本书是一本小波分析的入门书，着重于样条小波和时频分析．书中基本内容有Fourier分析、小波变换、尺度函数、基数样条分析、基数样条小波、小波级数、正交小波和小波包．本书内容安排由浅入深，算法推导详细，既有理论，又有应用背景．

目录

Preface ix

1 An Overview 1

1.1 From Fourier analysm to wavelet analysm 1

1.2 The integral wavelet transform and time-frequency analysis 6

1.3 Inversion formulas and duals 9

1.4 Classification of wavelets 13

1.5 Multiresolution analysis, splines, and wavelets 16

1.6 Wavelet decompositions and reconstructions 18

2 Fourier Analysis 23

2.1 Fourier and inverse Fourier transforms 23

2.2 Continuous-time convolution and the delta function 27

2.3 Fourier transform of square-integrable functions 32

2.4 Fourier series 36

2.5 Basic convergence theory and Poisson's summation formula 43

3 Wavelet Transforms and Time-Frequency Analysis 49

3.1 The G abor transform 50