Finite frames are special collections of vectors utilized in Harmonic Analysis and Digital
Signal Processing. In this thesis, geometric aspects and construction techniques
are considered for the family of k-vector frames in Fn = Rn or Cn sharing a fixed
frame operator (denoted Fk(E, Fn), where E is the Hermitian positive definite frame
operator), and also the subfamily of this family obtained by fixing a list of vector
lengths (denoted Fk
µ(E, Fn), where µ is the list of lengths).
The family Fk(E, Fn) is shown to be diffeomorphic to the Stiefel manifold Vn(Fk),
and Fk
µ(E, Fn) is shown to be a smooth manifold if the list of vector lengths µ satisfy
certain conditions. Calculations for the dimensions of these manifolds are also
performed. Finally, a new construction technique is detailed for frames in Fk(E, Fn)
and Fk
µ(E, Fn).
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1335 |
| Date | 15 May 2009 |
| Creators | Strawn, Nathaniel Kirk |
| Contributors | Dykema, Kenneth |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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