کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4605267 | 1631330 | 2011 | 12 صفحه PDF | دانلود رایگان |
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.
Journal: Applied and Computational Harmonic Analysis - Volume 30, Issue 3, May 2011, Pages 307-318