Application of the Rigged Hilbert Spaces into the Generalized Signals and Systems Theory: Practical Example

Signals and Systems Theory (SST) is an essential subject 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 to deal with more general concepts, leaving out a wide range of problems. The purpose of our work is to develop a Generalized Signals and Systems Theory (GSST) which can include many different problems in a rigorous mathematical way. The introduction of the Rigged Hilbert Spaces (RHS) is an important point regarding this mathematical rigorousness, unifying the ordinary functions and generalized functions under the same framework. A review of these concepts and the application of the RHS to a concrete physical problem is presented in this paper.