0 Inner Product Spaces 0.1 Motivation 0.2 Definition of Inner Product 0.3 The Spaces L2 and l2 0.4 Schwarz and Triangle Inequalitiea 0.5 Orthogonality 0.6 Linear Operators and Their Adjoints 0.7 Least Squares and Linear Predictive Coding 0.8 Exercises 1 Fourier Series 1.1 Tntroduction 1.2 Computation of Fourier Series 1.3 Oonvergence Theorems for Fourier Series 1.4 Exercises 2 The Fourier Transform 2.1 Informal Development of the Fourier Transform 2.2 Properties of the Fourier Transform 2.3 Linear Filters 2.4 The Sampling Theorem 2.5 The Uncertainty Principle 2.6 Exercises 3 Discrete Fourier Analysis 3.1 The Discrete Fourier Transform 3.2 Discrete Signals 3.3 Exercises 4 Haar Wavelet Analysis 4.1 Why Wavelet.s? 4.2 Haar Wavelets 4.3 Haar Decomposition and Reconstruction Algorithms 4.4 Summary 4. 5 Exercises 5 Multiresolution Analysis 5.1 The Multiresolution Framework 5.2 Implementing Decomposition and Reconstruction 5.5 Fourier T$ansform Criteria 5.4 Exercises 6 The Daubechies Wavelets 6.1 Daubechies's Construction 6.2 Olassification, Bvloments, and Smoothness 6.3 Computational Issues 6.4 The Scaling Function at Dyadic Points 6.5 Exercises 7 Other Wavelet Topics 7.1 Oomputational Complexity 7.2 Wavelets in Higher Dimensions 7.3 Relating Decomposition and Reconstruction 7.4 Wavelet Transform Appendix A Technical Matters A.1 Proof of the Fourier Inversion Formula A.2 Rigoroue Proof of Theorem 5.17 Appendix B Matlab Routines B.1 General Compression Routine B.2 Use of MATLAn's FFT Routine for Filtering aILcl Compression B.3 Sample Routines Using MATLAn's Wavelet Toolbox B.4 MATLAn Code for the Algorithms in Section 5.2 Bibliography Index
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