DOI
https://doi.org/10.25772/P980-5893
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