Staying rich: LTI systems which preserve signal richness

There are many ways to define richness of a discrete time signal. This paper considers a particular definition and explores the conditions under which a linear time invariant system preserves the richness property. Several examples are presented to clarify the issues involved in the problem. Some sufficient conditions are presented. Also presented are necessary and sufficient conditions for some special cases. A set of necessary and sufficient conditions for the most general case is not known at this time.