Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/21038
Title: | Alternate Duals of Gabor Subspace Frames |
Authors: | Akinlar, Mehmet Ali |
Advisor: | Gabardo, Jean-Pierre |
Department: | Mathematics and Statistics |
Keywords: | alterante duals, Gabor subspace frames, function, linear span, Bessel Collection, The Zak Transform |
Publication Date: | Aug-2005 |
Abstract: | <p> In this thesis we mainly give a characterization of dual frames of Gabor subspace frames. We give necessary and sufficient conditions for the existence and the uniqueness of a function h (called window) in the closed linear span of a Gabor subspace frame {EmbTnak}m,n∈Z such that the Bessel collection {EmbTnah}m,n∈Z serves as the dual frame of the original frame {EmbTnag}m,n∈Z. We solve the problem for three cases, first ab = 1, second ab = p ∈ N, and third ab = p/q, gcd(p, q) = 1. In each case, we first find the conditions for upper frame bound (known as Bessel collection). Secondly, we characterize the functions which are orthogonal to {EmbTnag}m,n∈Z in terms of the Zak transform, and then obtain necessary and sufficient conditions for lower frame bound. Here we state obtained conditions for normalized tight frame as a corollary. Finally, using all this information we solve the duality problem.</p> |
URI: | http://hdl.handle.net/11375/21038 |
Appears in Collections: | Digitized Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Akinlar_Mehmet_A._2005Aug_Masters..pdf | 2.08 MB | Adobe PDF | View/Open |
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