Properties of real and complex ETFs and their application to the design of low coherence frames

Certain properties of an equiangular tight frame are contained in the sign (or phase) of its corresponding Gram matrix. In this paper we convey new properties for Gram matrices of equiangular tight frames and use them to construct new frames with low average and worst case coherences. Based on these results, we also provide properties of the synthesis matrix of equiangular tight frames.