Keywords
Frames, Dual Frames, Vector Space, Hilbert Space, Functional Analysis, Discrete Gabor Frames, Gabor Analysis
Abstract
Since their discovery in the early 1950's, frames have emerged as an important tool in areas such as signal processing, image processing, data compression and sampling theory, just to name a few. Our purpose of this dissertation is to investigate dual frames and the ability to find dual frames which are optimal when coping with the problem of erasures in data transmission. In addition, we study a special class of frames which exhibit algebraic structure, discrete Gabor frames. Much work has been done in the study of discrete Gabor frames in Rn, but very little is known about the l2(Z) case or the l2(Zd) case. We establish some basic Gabor frame theory for l2(Z) and then generalize to the l2(Zd) case.
Notes
If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu
Graduation Date
2009
Advisor
Han, Deguang
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematics
Format
application/pdf
Identifier
CFE0002614
URL
http://purl.fcla.edu/fcla/etd/CFE0002614
Language
English
Release Date
May 2009
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Lopez, Jerry, "Optimal Dual Frames For Erasures And Discrete Gabor Frames" (2009). Electronic Theses and Dissertations. 3922.
https://stars.library.ucf.edu/etd/3922