Application of the Rigged Hilbert Spaces into the Generalized Signals & Systems Theory

Signals and Systems Theory (SST) plays a fundamental role in the educational and professional background of electrical engineering as well as in many other scientific areas. Many authors present this theory following a scheme which is valid for the analysis of general problems but they avoid dealing with more general concepts, leaving out a wide range of problems. The final purpose is to develop a Generalized Signals and Systems Theory (GSST) which can include many different problems in a rigorous way. An important point related to this mathematical rigorousness is the relation between the ordinary functions and generalized functions in infinite dimensional signal spaces through the Rigged Hilbert Spaces (RHS), which is presented in this paper.