Time domain representation of systems on bandlimited signals

Since the discovery of Shannonpsilas sampling theorem, signal and system representation has become an intense research topic. One task of system theory is to find efficient representations of signals and systems. In this paper time domain representations of stable linear time-invariant systems are analyzed. Although a frequency domain representation of such systems is always possible, the time domain representation is problematic. It is shown that the convolution integral diverges for certain systems and functions. Furthermore, we characterize the systems for which a time domain representation is possible by giving necessary and sufficient conditions for pointwise and uniform convergence.