Defense Date

2012

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Kevin Beanland

Abstract

The goal of this paper will be to study how frame theory is applied within the field of signal processing. A frame is a redundant (i.e. not linearly independent) coordinate system for a vector space that satisfies a certain Parseval-type norm inequality. Frames provide a means for transmitting data and, when a certain about of loss is anticipated, their redundancy allows for better signal reconstruction. We will start with the basics of frame theory, give examples of frames and an application that illustrates how this redundancy can be exploited to achieve better signal reconstruction. We also include an introduction to the theory of frames in infinite dimensional Hilbert spaces as well as an interesting example.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

May 2012

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