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Preface | ||
1 | Introduction | 1 |
1.1 | Signal Transformation | 1 |
1.2 | Orthogonal Transform | 4 |
1.3 | Frames in Vector Space | 8 |
1.4 | Time-Frequency Analysis | 13 |
1.5 | Applications of Time-Frequency Analysis | 20 |
2 | Principles of the Wavelet Transform | 23 |
2.2 | The Continuous Wavelet Transform | 32 |
2.3 | Discrete Parameter Wavelet Transform | 39 |
Appendix A - Resolution of the Identity | 50 | |
3 | Multiresolution Analysis, Wavelets and Digital Filters | 53 |
3.2 | The DPWT and MRA | 55 |
3.3 | Principles of MRA | 63 |
3.4 | Filters for Perfect Reconstruction | 74 |
3.5 | Paraunitary Filters and Orthonormal Wavelets | 83 |
3.6 | Filter Design for Orthonormal Wavelets | 89 |
3.7 | Biorthogonal Filters | 91 |
3.8 | Wavelet Construction from Two-Scale Equations | 94 |
3.9 | Two Dimensional Wavelets | 101 |
Appendix B - Theorem for Convergence of [Phi]([omega]) | 103 | |
Appendix C - Solution of a Polynomial in cos([omega]) | 108 | |
4 | Current Topics | 111 |
4.1 | Wavelet Packets | 111 |
4.2 | Discrete Time Wavelet Transform | 113 |
4.3 | Signal Processing Applications | 120 |
References | 125 | |
Index | 131 |
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Add Wavelet Basics, Since the study of wavelets is a relatively new area, much of the research coming from mathematicians, most of the literature uses terminology, concepts and proofs that may, at times, be difficult and intimidating for the engineer. Wavelet Basics has ther, Wavelet Basics to your collection on WonderClub |