dc.contributor.advisor | Larson, David | |
dc.creator | Henderson, Troy Lee, IV | |
dc.date.accessioned | 2006-10-30T23:32:16Z | |
dc.date.available | 2006-10-30T23:32:16Z | |
dc.date.created | 2005-08 | |
dc.date.issued | 2006-10-30 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/4392 | |
dc.description.abstract | 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. | en |
dc.format.extent | 403152 bytes | en |
dc.format.medium | electronic | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.publisher | Texas A&M University | |
dc.subject | Frames | en |
dc.subject | Bases | en |
dc.subject | Gram-Schmidt | en |
dc.title | Causal equivalence of frames | en |
dc.type | Book | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Smith, Roger | |
dc.contributor.committeeMember | Ward, Joe | |
dc.contributor.committeeMember | Wilhelm, Wilbert | |
dc.type.genre | Electronic Dissertation | en |
dc.type.material | text | en |
dc.format.digitalOrigin | born digital | en |