Chapter List

1.1. System Representation

A system is an organized set of components, of concepts whose role is to perform one or more tasks. The point of view adopted in the characterization of systems is to deal only with the input-output relations, with their causes and effects, irrespective of the physical nature of the phenomena involved.

Hence, a system realizes an application of the input signal space, modeling magnitudes that affect the behavior of the system, into the space of output signals, modeling relevant magnitudes for this behavior.

Figure 1.1: System symbolics

In what follows, we will consider mono-variable, analog or continuous systems which will have only one input and one output, modeled by continuous signals.

1.2. Signal Models

A continuous-time signal ( t ? R) is represented a priori through a function x ( t ) defined on a bounded interval if its observation is necessarily of finite duration.

When signal mathematical models are built, the intention is to artificially extend this observation to an infinite duration, to introduce discontinuities or to generate Dirac impulses, as a derivative of a step function. The most general...