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.

- Advisors
- Kwon, Kil-Hyun
*researcher*; 권길헌

- 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

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

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