dc.contributor.author |
Vale, Richard |
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dc.contributor.author |
Waldron, Shayne |
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dc.date.accessioned |
2009-08-28T03:22:27Z |
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dc.date.available |
2009-08-28T03:22:27Z |
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dc.date.issued |
2007-07 |
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dc.identifier.citation |
Department of Mathematics - Research Reports-559 (2007) |
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dc.identifier.issn |
1173-0889 |
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dc.identifier.uri |
http://hdl.handle.net/2292/5100 |
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dc.description.abstract |
Let $cH$ be a Hilbert space of finite dimension $d$, such as the finite signals $Cd$ or a space of multivariate orthogonal polynomials, and $nge d$. There is a finite number of tight frames of $n$ vectors for $cH$ which can be obtained as the orbit of a single vector under the unitary action of an abelian group $G$ (of symmetries of the frame). Each of these so called {it harmonic frames} or {it geometrically uniform frames} can be obtained from the character table of $G$ in a simple way. These frames are used in signal processing and information theory. For a nonabelian group $G$ there are in general uncountably many inequivalent tight frames of $n$ vectors for $cH$ which can be obtained as such a $G$--orbit. However, by adding an additional natural symmetry condition (which automatically holds if $G$ is abelian), we obtain a finite class of such frames which can be constructed from the character table of $G$ in a similar fashion to the harmonic frames. This is done by identifying each $G$--orbit with an element of the group algebra $CC G$ (via its Gramian), imposing the condition in the group algebra, and then describing the corresponding class of tight frames. |
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dc.publisher |
Department of Mathematics, The University of Auckland, New Zealand |
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dc.relation.ispartofseries |
Research Reports - Department of Mathematics |
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dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.source.uri |
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=559 |
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dc.title |
Tight frames generated by finite nonabelian groups |
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dc.type |
Technical Report |
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dc.subject.marsden |
Fields of Research::230000 Mathematical Sciences::230100 Mathematics |
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dc.rights.holder |
The author(s) |
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