Reconstruction from non-uniform samples

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Leow, Kwang Siong Jeremy

Advisor dc:contributor.advisor

• Alan V. Oppenheim.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/57688

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/57688