| Summary: | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. === Cataloged from PDF version of thesis. === Includes bibliographical references (p. 79-81). === Exact reconstruction of a band-limited signal from its non-uniform samples involves the use of Lagrange interpolation, which is impractical to implement as it is computationally difficult. This thesis develops approximate reconstruction methods based on time-warping to obtain reconstruction of band-limited signals from non-uniform samples. A review of non-uniform sampling theorems is presented followed by an alternative interpretation of the Lagrange interpolation kernel by decomposing the kernel into its constituent components. A discussion of time-warping and its use in the context of non-uniform sampling is made. This includes an alternative interpretation known as the delay-modulation, which we show to be a simpler representation for a specific case of non-uniform sampling where the sample instants are deviations from a uniform grid. Based on some essential characteristics of the Lagrange kernel, a framework using a modulated time-warped sine function is formed to obtain various approximations to the Lagrange kernel. The thesis also formulates a vector space representation of non-uniform sampling and interpolation and incorporates warped sinc functions to obtain faster convergence in iterative algorithms for reconstruction of band-limited signals from non-uniform samples. === by Kwang Siong Jeremy Leow. === S.M.
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