On the realization of band-pass type systems for bounded bandlimited signals

In this paper we analyze band-pass type systems that operate on bounded bandlimited signals. For a very general class of band-pass type systems, we prove that there exists no linear realization of the systems in this class. Since ideal band-pass type systems are included in this class, it follows that there exists no linear realization of ideal band-pass type systems. This result is obtained under very general assumptions. For example, we do not assume the systems to be time-invariance. Finally, it is shown that a non-linear realization of band-pass type systems is possible.