Complex equiangular tight frames

Joel A. Tropp

doi:10.1117/12.618821

30 August 2005 Complex equiangular tight frames

Joel A. Tropp

Proceedings Volume 5914, Wavelets XI; 591401 (2005) https://doi.org/10.1117/12.618821
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

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).

Citation Download Citation

Joel A. Tropp "Complex equiangular tight frames", Proc. SPIE 5914, Wavelets XI, 591401 (30 August 2005); https://doi.org/10.1117/12.618821

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available