Balanced frames: a useful tool in signal processing with good properties

Sigrid B. Heineken, Patricia M. Morillas, Pablo Tarazaga

Published 2019-04-01Version 1

So far there has not been paid attention in the literature to frames that are balanced, i.e. those frames which sum is zero. In this paper we study balanced frames, and in particular balanced unit norm tight frames in finite dimensional Hilbert spaces. We discuss their various advantages in signal processing, describe their fundamental properties and finally, present several examples and methods for constructing them. Unit norm tight frames play a central role in frame theory and its applications. We show that balanced unit norm tight frames turn out to perform better than the non balanced ones.