A novel basis of dynamical systems and its application to desampling

This paper provides a novel basis of dynamical systems. The basis involves a new signal space consisting of real-valued signals and discrete moment signals expressed by real time functions and delta function series, respectively, a notation of uniform rate sampling in the space, a method to distinguish among system classes, novel names of conceivable sorts of dynamical linear or discretely linear systems and a unified representation of these systems. To demonstrate the availability of the basis, a system model, with sampling, of a 0-th order hold element is shown and extended to those of approximate circuits of ideal low-pass filters. Finally, conventional sampled-data system models of interpolating circuits are denied because of false counter-examples of Shannon's sampling theorem.