Prime tight frames

Details Prime tight frames Prime tight frames

2012-02-28

arxiv.org/abs/1202.6350v2

Mathematics

Functional Analysis

v2: Section 3.1 shortened and reordered

Scientific paper

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. We show that finite tight frames can be written as a union of prime tight frames. In addition, we show that when they exist, equiangular tight frames are prime tight frames. We then examine two families of well-known tight frames vis-a-vis the notion of prime tight frames. More specifically, we characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method. As a byproduct of this last result, we obtain a characterization of when the tetris construction works for redundancies below two.

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