Cyclic frames in finite-dimensional Hilbert spaces

TL;DR

This paper investigates cyclic frames in finite-dimensional Hilbert spaces, providing new characterizations that enhance understanding of their structure and properties, especially regarding their application in erasure problems.

Contribution

It offers a novel characterization of cyclic frames and dynamical frames, expanding theoretical understanding and potential applications in signal processing.

Findings

New characterization of dynamical frames

Enhanced understanding of cyclic frames

Implications for erasure resilience

Abstract

Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi et al. in \cite{ACM} and subsequent papers; they are particularly interesting due to their attractive properties in the context of erasure problems. By applying an alternative approach, we are able to shed new light on general dynamical frames as well as cyclic frames. In particular, we provide a characterization of dynamical frames, which in turn leads to a characterization of cyclic frames.