Wavelets via their fourier transforms = 푸리에 변환으로 정의되는 웨이브릿

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
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=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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