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.
Author(s): Martin J. Mohlenkamp and Maria Cristina Pereyra
Series: Ems Series of Lectures in Mathematics
Publisher: European Mathematical Society
Year: 2008
Language: English
Pages: 120
Tags: Приборостроение;Обработка сигналов;Вейвлет-анализ;
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
