Defense Date


Document Type


Degree Name

Master of Science


Mathematical Sciences

First Advisor

Kevin Beanland


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.


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Date of Submission

May 2012