Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems

Abstract

Dynamical sampling is a new type of sampling problem that results from sampling an evolving signal at various times and asks the question: when do coarse samplings taken at varying times contain the same information as a finer sampling taken at the earliest time? In other words, under what conditions on an evolving system, can time samples be traded for spatial samples? In this dissertation, this problem is answered for evolution rules given by convolution and sampling sets that are quasi-uniform. The problem is studied in finite dimensions, infinite dimensions, and shift-invariant spaces.