Frames have recently become popular in the area of applied mathematics known
as digital signal processing. Frames offer a level of redundancy that bases do not
provide. In a sub-area of signal processing known as data recovery, redundancy has
become increasingly useful; therefore, so have frames. Just as orthonormal bases are
desirable for numerical computations, Parseval frames provide similar properties as
orthonormal bases while maintaining a desired level of redundancy. This dissertation
will begin with a basic background on frames and will proceed to encapsulate my
research as partial fulfillment of the requirements for the Ph.D. degree in Mathematics
at Texas A&M University. More specifically, in this dissertation we investigate an
apparently new concept we term causal equivalence of frames and techniques for
transforming frames into Parseval frames in a way that generalizes the Classical Gram-
Schmidt process for bases. Finally, we will compare and contrast these techniques.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4392 |
| Date | 30 October 2006 |
| Creators | Henderson, Troy Lee, IV |
| Contributors | Larson, David |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 403152 bytes, electronic, application/pdf, born digital |
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