Wavelet Basics - Chan, Y. T.

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Résumé :
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 therefore been written as an introductory book for scientists and engineers. The mathematical presentation has been kept simple, the concepts being presented in elaborate detail in a terminology that engineers will find familiar. Difficult ideas are illustrated with examples which will also aid in the development of an intuitive insight. Chapter 1 reviews the basics of signal transformation and discusses the concepts of duals and frames. Chapter 2 introduces the wavelet transform, contrasts it with the short-time Fourier transform and clarifies the names of the different types of wavelet transforms. Chapter 3 links multiresolution analysis, orthonormal wavelets and the design of digital filters. Chapter 4 gives a tour d'horizon of topics of current interest: wavelet packets and discrete time wavelet transforms, and concludes with applications in signal processing.

Sommaire:
1. Introduction.- 1.1 Signal Transformation.- 1.2 Orthogonal Transform.- 1.3 Frames in Vector Space.- 1.4 Time-Frequency Analysis.- 1.5 Applications of Time-Frequency Analysis.- 2. Principles of the Wavelet Transform.- 2.1 Introduction.- 2.2 The Continuous Wavelet Transform.- 2.3 Discrete Parameter Wavelet Transform.- Appendix A - Resolution of the Identity.- 3. Multiresolution Analysis, Wavelets and Digital Filters.- 3.1 Introduction.- 3.2 The DPWT and MRA.- 3.3 Principles of MRA.- 3.4 Filters for Perfect Reconstruction.- 3.5 Paraunitary Filters and Orthonormal Wavelets.- 3.6 Filter Design for Orthonormal Wavelets.- 3.7 Biorthogonal Filters.- 3.8 Wavelet Construction from Two-Scale Equations.- 3.9 Two Dimensional Wavelets.- Appendix B - Theorem for Convergence of ?(?).- Appendix C - Solution of a Polynomial in cos(?).- 4. Current Topics.- 4.1 Wavelet Packets.- 4.2 Discrete Time Wavelet Transform.- 4.3 Signal Processing Applications>.- References.