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[电子工程] Fundamentals of wavelets Theory, algorithms, and applications.

Fundamentals of wavelets Theory, algorithms, and applications.

Fundamentals of wavelets Theory, algorithms, and applications.

book 收藏 
 作者 JAIDEVA C. GOSWAMI
 ISBN 978-0-471-19748-5
 出版日期/版本 1999/1st edition
 格式 其它

主题内容

The concept of wavelet analysis has been in place in one form or another since the beginning of the twentieth century. The Littlewood-Paley technique and Calderon- Zygmund theory in harmonic analysis and digital filter bank theory in signal pro- processing can be considered as forerunners of wavelet analysis. However, in its present form, wavelet theory attracted attention in the 1980s through the work of several researchers from various disciplines—Stromberg, Morlet, Grossmann, Meyer, Bat- Battle, Lemarie, Coifrnan, Daubechies, Mallat, Chui—to name a few. Many other re- researchers have also made significant contributions. In applications to discrete data sets, wavelets may be considered as basis functions generated by dilations and translations of a single function. Analogous to Fourier analysis, there are wavelet series (WS) and integral wavelet transforms (IWTs). In wavelet analysis, WS and IWTs are intimately related. The IWT of a finite-energy function on the real line evaluated at certain points in the time-scale domain gives the coefficients for its wavelet series representation. No such relation exists between Fourier series and Fourier transform, which are applied to different classes of func- functions; the former is applied to finite-energy periodic functions, whereas the latter is applied to functions that have finite energy over the real line. Furthermore, Fourier analysis is global in the sense that each frequency (time) component of the function is influenced by all the time (frequency) components of the function. On the other hand, wavelet analysis is a local analysis. This local nature of wavelet analysis makes it suitable for time-frequency analysis of signals.
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