A friendly guide to wavelets
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書誌事項
A friendly guide to wavelets
Birkhäuser, 1994
- : us
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注記
Bibliography: p. [291]-296
Icludes index
内容説明・目次
- 巻冊次
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: us ISBN 9780817637118
内容説明
This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption. Chapters 10 and 11 consist of original research and are written in a more advanced style. In Chapter 10 it is shown that the structure of Maxwell's equations implies the existence of a wavelet analysis specifically adopted to electromagnetic radiation. The associated 'eletromagnetic wavelets' are pulses parameterized by their point of origin and their scale, and can be made arbitrarily short by choosing fine scales.
Furthermore, it is shown that every electromagnetic wave can be composed of such localized wavelets. This is applied in Chapter 11 to give a new formulation of radar based on electromagnetic wavelets. Since this theory is fully relativistic, its description of the Doppler effect is exact. In particular, it is three-dimensional, and does not make the usual assumption that the outgoing signal has a narrow bandwidth. Thus it should be useful in the construction of ultra-wideband radar systems.
目次
Preface.- Suggestions to the Reader.- Symbols, Conventions, and Transforms.- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation.- Windowed Fourier Transforms.- Continuous Wavelet Transforms.- Generalized Frames: Key to Analysis and Synthesis.- Discrete Time-Frequency Analysis and Sampling.- Discrete Time-Scale Analysis.- Multiresolution Analysis.- Daubechies' Orthonormal Wavelet Bases.- Part II: Physical Wavelets.- Introduction to Wavelet Electromagnetics.- Applications to Radar and Scattering.- Wavelet Acoustics.- References.- Index.
- 巻冊次
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ISBN 9783764337117
内容説明
This volume is intended to serve as a textbook for a one-term introductory course on wavelet analysis. It includes the following chapters: windowed Fourier transforms; algebraic construction of Daubechies' wavelets bases; and regulatory and vanishing moments.
目次
- Preliminaries - background and notation
- windowed Fourier transforms
- continuous wavelet transforms
- general frames - the key to analysis and synthesis
- discrete frames and sampling theorems
- oversampling
- reproducing kernals and consistency
- algebraic construction of Daubechies' wavelets bases
- an operational calculus for decomposition and reconstruction
- convergence of wavelet series
- regularity and vanishing moments.
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