Computing Upper and Lower Bounds for the Bandwidth of Bandlimited Signals

Abstract

The bandwidth of a signal is an important physical property that is of relevance in many signal processing applications. In this paper we study questions related to the computability of the bandwidth of bandlimited signals. To this end we employ the concept of Turing computability, which exactly describes what is theoretically feasible and can be computed on a digital machine. Recently, it has been shown that there exist bandlimited signals, the actual bandwidth of which cannot be algorithmically determined, i.e., computed on a digital machine. In this work, we consider the most general class of bandlimited signals and analyze whether it is at least possible to compute nontrivial upper or lower bounds for the actual bandwidth of its members. We show that this is not possible in general.