<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> / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21038 |
| Date | 08 1900 |
| Creators | Akinlar, Mehmet Ali |
| Contributors | Gabardo, Jean-Pierre, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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