A complex equiangular tight frame (ETF) is a tight frame consisting of N unit vectors in C^d whose absolute inner products are identical. One may view complex ETFs as a natural geometric generalization of an orthonormal basis. Numerical evidence suggests that these objects do not arise for most pairs (d, N). The goal of this paper is to develop conditions on (d, N) under which complex ETFs can exist. In particular, this work concentrates on the class of harmonic ETFs, in which the components of the frame vectors are roots of unity. In this case, it is possible to leverage field theory to obtain stringent restrictions on the possible values for (d, N).

Date Published: 30 August 2005
PDF: 11 pages
Proc. SPIE 5914, Wavelets XI, 591401 (30 August 2005); doi: 10.1117/12.618821

Published in SPIE Proceedings Vol. 5914:
Wavelets XI
Manos Papadakis; Andrew F. Laine; Michael A. Unser, Editor(s)