Geometry and constructions of finite frames /
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis eBook |
| Language: | English |
| Published: |
[College Station, Tex.] :
[Texas A&M University],
[2010]
|
| Subjects: | |
| Online Access: | Link to OAK Trust copy |
| Abstract: | 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 æ(E, Fn), where ℗æ is the list of lengths). The family Fk(E, Fn) is shown to be diffeomorphic to the Stiefel manifold Vn(Fk), and Fk ℗æ(E, Fn) is shown to be a smooth manifold if the list of vector lengths ℗æ 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 ℗æ(E, Fn). |
|---|---|
| Item Description: | "Major Subject: Mathematics" Title from author supplied metadata (automated record created 2010-03-12 12:08:51). Electronic resource. |
| Physical Description: | 1 online resource. |
| Bibliography: | Includes bibliographical references. |