Geometry and constructions of finite frames

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Title: Geometry and constructions of finite frames
Author: Strawn, Nathaniel Kirk
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 ? (E , Fn ) , where ? is the list of lengths ) . The family Fk (E , Fn ) is shown to be diffeomorphic to the Stiefel manifold Vn (Fk ) , and Fk ? (E , Fn ) is shown to be a smooth manifold if the list of vector lengths ? 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 ? (E , Fn ) .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -1335
Date: 2009-05-15

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Geometry and constructions of finite frames. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -1335 .

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