Extensions of the Signal Richness Preservation Problem in LTI Systems

The idea of signal richness has recently been studied in considerable details, and the conditions on linear time invariant (LTI) systems to preserve such richness have been established. In this paper, the concept of richness is extended to practically useful classes such as bounded signals. The class of LTI systems studied for the richness preservation problem are generalized to cases including rectangular systems and infinite impulse response (IIR) systems. Structured proofs of the newly found necessary and sufficient conditions are also presented