Effective Approximation Of Bandlimited Signals And Their Samples

Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the computability of the signal. Computability is important in order that the approximation error can be controlled. We show that the computability of the signal is not always preserved. Further, we provide a simple necessary and sufficient condition for the computability of the continuous-time signal, and a simple canonical algorithm that can be used for the computation.