(The) stability of integer translations of a function and its application to MRA construction함수의 정수 이동의 안정성과 MRA에의 응용

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This thesis is devoted to the study of the stability of integer translates of a function and sampling functions and its applications to multiresolution analysis (MRA) construction. First, we review the concept of MRA and give some important results on MRA. We also study the stability of the integer translates of the characteristic functions of one interval and the functions whose Fourier transforms are the characteristic functions of one interval. Next, we improve the well-known Cohen`s theorem using the concept of ``congruence to [-π,π] modulo 2π" for the refinable stable functions by modifying the set [-π,π]. We characterize the orthonormal scaling functions of length of support less than 5 by applying the Cohen`s cycle theorem. We also show that the preservation of stability under the convolution is related with the zero set of the Fourier transform of inducing stable function and the preservation of stability for compactly supported refinable function is related with the zero set of its mask. Finally, we give a necessary and sufficient condition for a refinable sampling functions which connects the sampling function and stable function. We also give the dual functions of sampling functions, a method of constructing the sampling function in $V_1$ instead of $V_0$, and some examples.
Advisors
Kim, Hong-Ohresearcher김홍오researcher
Description
한국과학기술원 : 응용수학전공,
Publisher
한국과학기술원
Issue Date
2002
Identifier
174569/325007 / 000965395
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 응용수학전공, 2002.2, [ [ii], 57 p. ]

Keywords

wavelet; stability; sampling function; 표본함수; 소파동; 안정성; MRA

URI
http://hdl.handle.net/10203/41849
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=174569&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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