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

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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)

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Included in

Mathematics Commons

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