Equiangular frames and generalizations of the Welch bound to dual pairs of frames

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The purpose of this paper is twofold. First, we determine the lower bound for the maximum coherence between a pair of dual frames in and state conditions under which the lower bound is attained. It is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. For the case where an equiangular dual cannot be found we provide conditions under which the number of angles among vectors in the canonical dual frame is small.
Original languageEnglish
JournalLinear and Multilinear Algebra
Pages (from-to)1-11
ISSN1563-5139
DOIs
Publication statusPublished - 2019
CitationsWeb of Science® Times Cited: No match on DOI

    Research areas

  • Dual frames, Equiangular frames, Tight frames, Welch bound

ID: 172824665