DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Hong-Oh | - |
dc.contributor.advisor | 김홍오 | - |
dc.contributor.author | Park, Jong-Ha | - |
dc.contributor.author | 박종하 | - |
dc.date.accessioned | 2011-12-14T04:38:47Z | - |
dc.date.available | 2011-12-14T04:38:47Z | - |
dc.date.issued | 1998 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=144198&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41805 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학과, 1998.8, [ [86] p. ] | - |
dc.description.abstract | 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. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Wavelets | - |
dc.subject | Fourier transform | - |
dc.subject | 푸리에 변환 | - |
dc.subject | 웨이블릿 | - |
dc.title | Wavelets via their fourier transforms | - |
dc.title.alternative | 푸리에 변환으로 정의되는 웨이브릿 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 144198/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000955144 | - |
dc.contributor.localauthor | Kim, Hong-Oh | - |
dc.contributor.localauthor | 김홍오 | - |
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