  The bandwidth of a signal is an important physical property that is of
relevance in many signal- and information-theoretic applications. In this paper
we study questions related to the computability of the bandwidth of computable
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 computer. Recently, it has been shown that there exist computable
bandlimited signals with finite energy, the actual bandwidth of which is not a
computable number, and hence cannot be computed on a digital computer. In this
work, we consider the most general class of band-limited signals, together with
different computable representations thereof. Among other things, our analysis
includes a characterization of the arithmetic complexity of the bandwidth of
such signals and yields a negative answer to the question of whether it is at
least possible to compute non-trivial upper or lower bounds for the bandwidth
of a bandlimited signal. Furthermore, we relate the problem of bandwidth
computation to the theory of oracle machines. In particular, we consider
halting and totality oracles, which belong to the most frequently investigated
oracle machines in the theory of computation.
