#### Signal reconstruction from nonideal samples on shift-invariant spaces = 이동불변공간에서의 비이상 샘플을 통한 신호 복원

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This dissertation handled sampling theorems for nonideal samples on shift-invariant spaces: irregular sampling and consistent sampling. For irregualr sampling, let $V(\phi)$ be a shift invariant subspace of $L^{2}(\mathbb{R})$ with a Riesz or frame generator $\phi(t)$. We take $\phi(t)$ suitably so that the regular sampling expansion : $f(t) = \sum\limits_{n\in \mathbb{Z}}f(n)S(t-n)$ holds on $V(\phi)$. We then find conditions on the generator $\phi(t)$ and various bounds of the perturbation $\{ \delta _n \}_{n \in \mathbb{Z}}$ under which an irregular sampling expansion \begin{equation*} f(t)=\sum_{n \in \mathbb{Z}} f(n+ \delta_n)S_n(t) \end{equation*} holds on $V(\phi)$. We also consider the approximate consistent sampling process in the space $L^2(\mathbb{R})$ of signals of finite energy. The consistency means that the original signal and its approximation have the same measurements. We assume that sampling and reconstruction functions $\{\psi_i\}_{i=1}^M$, $\{\phi_j\}_{j=1}^N$ are given as Riesz generators and the measurements $\{\langle f(t),\psi_i(t-qk)\rangle |1\leq i \leq M, k\in\mathbb{Z}\}$ are given as inner-products between the input signal and the sampling functions with rational sampling rate $q=\frac{m}{n}$. We then find an approximation in the reconstruction space $V(\Phi)$, the shift-invariant space generated by the reconstruction functions, which is consistent with the input signal. We also discuss some relevant properties such as the performance analysis of the consistent approximation.
Kwon, Kil-Hyunresearcher권길헌
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2013
Identifier
513602/325007  / 020085146
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2013.2, [ iii, 42 p. ]

Keywords

shift-invariant space; irregular sampling; consistent sampling; Riesz basis; 이동불변공간; 불균등 샘플링; consistent 샘플링; 리츠 기저; 프레임; frame

URI
http://hdl.handle.net/10203/181550