Wavelets via their fourier transforms = 푸리에 변환으로 정의되는 웨이브릿

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As the most simple examples of wavelets and scaling functions which are expressed in terms of their Fourier transforms, we construct and study the generalized Shannon wavelets (G-Shannon wavelets) and the generalized Shannon scaling functions (G-Shannon scaling functions) whose Fourier transforms are given by characteristic functions. One of the features of the G-Shannon wavelets is that they may or may not be associated with MRA. We characterize those G-Shannon wavelets which can be associated with MRA and give a criterion to determine whether a wavelet from a class of G-Shannon wavelets of Ha et al. can be associated with MRA or not. Another feature of the G-Shannon wavelets is the convergence of a G-Shannon wavelet expansion influenced by the slow decay of the G-Shannon wavelets. We study the pointwise convergence and the Gibbs phenomenon on the G-Shannon wavelet expansions. In contrast to the regular wavelet expansion, there is a continuous function whose G-Shannon wavelet expansion diverges. We also see that the G-Shannon wavelet is a sampling function and has the corresponding sampling theorem. By the smoothing procedure of Meyer, the generalized Meyer wavelet is constructed from the G-Shannon wavelet which has a fast decay and satisfies an oversampling theorem.
Advisors
Kim, Hong-Ohresearcher김홍오researcher
Description
한국과학기술원 : 수학과,
Publisher
한국과학기술원
Issue Date
1998
Identifier
144198/325007 / 000955144
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학과, 1998.8, [ [86] p. ]

Keywords

Wavelets; Fourier transform; 푸리에 변환; 웨이블릿

URI
http://hdl.handle.net/10203/41805
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=144198&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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