信號(hào)處理的小波導(dǎo)引

內(nèi)容概要

本書(shū)取材于作者在多所國(guó)際知名大學(xué)講授”小波信號(hào)處理”課程時(shí)的講義，作者以信號(hào)處理的問(wèn)題為背景，用淺顯的數(shù)學(xué)語(yǔ)言闡述小波理論及應(yīng)用，使讀者可以透過(guò)復(fù)雜的數(shù)學(xué)公式來(lái)窺探小波的精髓，但又不致陷入小波純數(shù)學(xué)理論的迷宮。 
    本書(shū)既可以讓計(jì)算機(jī)及電子工程系的學(xué)生了解工程問(wèn)題的數(shù)學(xué)描述．又可以讓數(shù)學(xué)系的學(xué)生了解數(shù)學(xué)公式的工程意義，是一本極有價(jià)值的教材及參考書(shū)。

作者簡(jiǎn)介

Stephane Mallat是紐約大學(xué)Courant學(xué)院計(jì)算機(jī)科學(xué)系的教授，法國(guó)巴黎Ecole理工大學(xué)應(yīng)用數(shù)學(xué)系的教授，并兼任麻省理工學(xué)院電子工程系以及特拉維夫大學(xué)應(yīng)用數(shù)學(xué)系的客座教授。 Mallat博士還曾榮獲 ·1990年IEEE信號(hào)處理學(xué)會(huì)評(píng)選的論文獎(jiǎng)。 ·1993年“斯隆”數(shù)學(xué)研究基金

書(shū)籍目錄

PREFACEPREFACE TO THE SECOND EDITION NOTATION I INTRODUCTION TO A TRANSIENT WORLD  1.1 Fourier Kingdom  1.2 Time-Frequency Wedding    1.2.1 Windowed Fourier Transform    1.2.2 Wavelet Transform  1.3 Bases of Time-Frequency Atoms    1.3.1 Wavelet Bases and Filter Banks    1.3.2 Tilings of Wavelet Packet and Local Cosine Bases  1.4 Bases for What?   1.4.1 Approximation   1.4.2 Estimation   1.4.3 Compression  1.5 Travel Guide   1.5.1 Reproducible Computational Science   1.5.2 Road MapII FOURIER KINGDOM  2.1 Linear Time-Invariant Filtering   2.1.1 Impulse Response   2.1.2 Transfer Functions  2.2 Fourier Integrals   2.2.1 Fourier Transform in L1(R)   2.2.2 Fourier Transform in L2(R)   2.2.3 Examples  2.3 Properties   2.3.1 Regularity and Decay   2.3.2 Uncertainty Principle   2.3.3 Total Variation  2.4 Two-Dimensional Fourier Transform  2.5 ProblemsIII DISCRETE REVOLUTION  3.1 Sampling Analog Signals   3.1.1 Whittaker Sampling Theorem   3.1.2 Aliasing   3.1.3 General Sampling Theorems  3.2 Discrete Time-Invariant Filters   3.2.1 Impulse Response and Transfer Function   3.2.2 Fourier Series  3.3 Finite Signals   3.3.1 Circular Convolutions   3.3.2 Discrete Fourier Transform   3.3.3 Fast Fourier Transform   3.3.4 Fast Convolutions  3.4 Discrete Image Processing  3.5 ProblemsIV TIME MEETS FREQUENCY  4.1 Time-Frequency Atoms  4.2 Windowed Fourier Transform   4.2.1 Completeness and Stability   4.2.2 Choice of Window 2   4.2.3 Discrete Windowed Fourier Transform  4.3 Wavelet Transforms   4.3.1 Real Wavelets   4.3.2 Analytic Wavelets   4.3.3 Discrete Wavelets  4.4 Instantaneous Frequency  4.5 Quadratic Tune-Frequency Energy  4.6 ProblemsV FRAMES  5.1 Frame Theory  5.2 Windowed Fourier Frames  5.3 Wavelet Frames  5.4 Translation Invariance  5.5 Dyadic Wavelet Transform  5.6 ProblemsVI WAVELET ZOOM  6.1 Lipschitz Regularity  6.2 Wavelet Transform Modulus Maxima  6.3 Multiscale Edge Detection  6.4 Multifractals  6.5 ProblemsVII WAVELET BASES  7.1 Orthogonal Wavelet Bases  7.2 Classes of Wavelet Bases  7.3 Wavelets and Filter Banks  7.4 Biorthogonal Wavelet Bases  7.5 Wavelet Bases on an Interval IX AN APPROXIMATION TOUR  9.1 Linear Approximations  9.2 Non-Linear Approximations  9.3 Image Approximations with Wavelets  9.4 Adaptive Basis Selection ESTIMATIONS ARE APPROXIMATIONSXI TRANSFORM CODINGAppendix A MATHEMATICAL COMPLEMENTSAppendix B SOFTWARE TOOLBOXESBIBLIOGRAPHYINDEX

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