We present a new infinite family of full spark equal norm tight frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a cyclic group by a group of automorphisms. The only previously known algebraically constructed infinite families were the harmonic, Gabor and Dihedral frames. Our construction hinges on a theorem that requires no group structure. Additionally, we illustrate our results by providing explicit constructions of full spark frames.

中文翻译：

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制图表达轨道中的完整火花帧

我们提出了一个新的无穷大的全火花相等范数紧框架，它由一个a群表示引起，并且在有限的维度上是有限的，其中基础群是一个循环群与一组自同构的半直接乘积。以前唯一已知的由代数构造的无限族是谐波，Gabor和二面体框架。我们的构造取决于一个不需要群结构的定理。此外，我们通过提供完整火花框架的显式构造来说明我们的结果。