dc.contributor.author |
Waldron, Shayne |
en |
dc.contributor.author |
Chien, T-Y |
en |
dc.date.accessioned |
2012-03-13T20:32:39Z |
en |
dc.date.issued |
2011 |
en |
dc.identifier.citation |
Applied and Computational Harmonic Analysis 30(3):307-318 2011 |
en |
dc.identifier.issn |
1063-5203 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/14202 |
en |
dc.description.abstract |
Up to unitary equivalence, there are a finite number of tight frames of n vectors for Cd which can be obtained as the orbit of a single vector under the unitary action of an abelian group G (for nonabelian groups there may be uncountably many). These so called harmonic frames (or geometrically uniform tight frames) have recently been used in applications including signal processing (where G is the cyclic group). In an effort to find optimal harmonic frames for such applications, we seek a simple way to describe the unitary equivalence classes of harmonic frames. By using Pontryagin duality, we show that all harmonic frames of n vectors for Cd can be constructed from d-element subsets of G (|G|=n). We then show that in most, but not all cases, unitary equivalence preserves the group structure, and thus can be described in a simple way. This considerably reduces the complexity of determining whether harmonic frames are unitarily equivalent. We then give extensive examples, and make some steps towards a classification of all harmonic frames obtained from a cyclic group. |
en |
dc.publisher |
Elsevier Inc |
en |
dc.relation.ispartofseries |
Applied and Computational Harmonic Analysis |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from: http://www.sherpa.ac.uk/romeo/issn/1063-5203/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
A classification of the harmonic frames up to unitary equivalence |
en |
dc.type |
Journal Article |
en |
dc.identifier.doi |
10.1016/j.acha.2010.09.00 |
en |
pubs.issue |
3 |
en |
pubs.begin-page |
307 |
en |
pubs.volume |
30 |
en |
dc.rights.holder |
Copyright: Elsevier Inc |
en |
pubs.end-page |
318 |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
259862 |
en |
pubs.org-id |
Science |
en |
pubs.org-id |
Mathematics |
en |
pubs.record-created-at-source-date |
2011-12-13 |
en |