Wavelets, Their Friends, and What They Can Do for You (Ems Series of Lectures in Mathematics)

These notes introduce the central concepts surrounding wavelets and their applications. By focusing on the essential ideas and arguments, the authors enable readers to get to the heart of the matter as quickly as possible. A list of references guides readers interested in further study to the appropriate places in the literature for detailed proofs and real applications. The authors begin with the notion of time-frequency analysis, present the multiresolution analysis and basic wavelet construction, introduce the many friends, relatives, and mutations of wavelets, and finally give a selection of applications. This book is suitable for beginning graduate students and above. A preliminary chapter containing some of the prerequisite concepts and definitions is included for reference. So What Is All The Fuss About Wavelets? You Can Find Out By Reading These Notes. They Will Introduce You To The Central Concepts Surrounding Wavelets And Their Applications. By Focusing On The Essential Ideas And Arguments, They Enable You To Get To The Heart Of The Matter As Quickly As Possible. They Then Point You To The Appropriate Places In The Literature For Detailed Proofs And Real Applications, So You Can Continue Your Study. They Begin With The Notion Of Time-frequency Analysis, Present The Multiresolution Analysis And Basic Wavelet Construction, Introduce You To The Many Friends, Relatives And Mutations Of Wavelets, And Finally Give A Selection Of Applications. They Are Suitable For Beginning Graduate Students And Above. A Preliminary Chapter Containing Some Of The Prerequisite Concepts And Definitions Is Included For Reference.--jacket. Time-frequency Analysis -- Multiresolution Analysis And Wavelets -- Friends, Relatives, And Mutations Of Wavelets -- Assorted Applications. Martin J. Mohlenkamp, María Cristina Pereyra. Includes Bibliographical References (p. [95]-106) And Index. Preface......Page 6 Plain bases and unconditional bases......Page 12 Orthogonal bases and frames......Page 16 Orthogonal projections and complements......Page 19 Fourier analysis......Page 21 The windowed Fourier transform and Gabor bases......Page 29 Local trigonometric expansions......Page 34 The wavelet transform......Page 38 Multiresolution analysis......Page 42 The Haar wavelet and MRA......Page 45 Algorithm: The fast wavelet transform......Page 49 Daubechies style wavelets......Page 53 Other plain wavelets......Page 63 Biorthogonal MRA and wavelets......Page 65 Multiwavelets......Page 71 Wavelets in 2-D......Page 75 Wavelet packets......Page 76 Second generation wavelets......Page 78 An alternative localization notion and the prolate spheroidal wave functions.......Page 86 Signal/image processing......Page 88 Calculus with wavelets......Page 91 Applications to functional analysis......Page 95 Applications to differential equations......Page 99 References and further reading......Page 103 Internet references......Page 106 Index......Page 108