Abstract

The analysis of the linear systems as well as of the signals that interact with the different elements of the system and the environment that surrounds it, requires a clear knowledge of the mathematical analysis and especially of what is known as operational calculation, as of the operational calculation it is possible, in some cases, to facilitate the search for the solutions of the problems of analysis that are raised in the investigation of the systems represented by mathematical models. Both the mathematical models that represent the systems and the signals can be defined in terms of continuous or discrete variables, for which each of these points of view requires its corresponding model, and the determination of its solution to the problem will be based on the domain over which the model is represented, whether continuous or discrete, as well as the concepts used in the spectral domain. The author assumes that the reader has a clear knowledge of Laplace, Fourier and Z transform, which are used as alternative tools for the analysis of problems in the domain where the mathematical models are described. On the other hand, brief explanations of some differential equation solving methods are presented in this book, which represent the relationships among the variables of the dynamic system defined in the continuous domain that is being studied. The purpose of introducing differential equations is to induce the method of solving difference equations, which are used as mathematical models of dynamic systems seen from a discrete domain perspective. It is important to note that the scope of this work does not include the analysis of linear systems from the stochastic perspective, because this approach requires clear knowledge of the probabilities and stochastic processes, and that this material It should form the textbook of the undergraduate course of Analysis of Linear Systems of the School of Electrical Engineering of the Central University of Venezuela, and this course studies the systems from the deterministic point of view. It should be noted that the author has used, in a very careful way, a notation that allows to discriminate clearly when the mathematical models are referred to the continuous or discrete domain. Moreover, the author makes a clear difference, in the case of the signals defined in the discrete domain, between what a function in the discrete domain means and its corresponding sequence of samples, both of which are used for the representation of the signals in the domain of discrete domain. In addition, the author has tried as far as possible to refer to the domain, without this being limited to the domain in continuous or discrete time, because in the opinion of the author, the concepts, methods and theoretical bases should not refer exclusively to the domain of time, but to any domain, thus leaving the possibility of generalizing the application of what is presented in the work, although in the area of Electrical Engineering it is very common to see the models and signals defined in the domain of time and frequency. It is appropriate to establish that throughout the work, the signals studied and their use in the analysis of the various systems, both in the continuous and discrete domain, are considered real. That is, they are signals that represent measures in the set of real numbers, or in mathematical terms are signals represented by functions whose ranges correspond to the set of real numbers. In addition, it must be taken into account that the signals are modeled by functions defined in the domain of real or integer numbers, depending on whether the signals represent measurements in the continuous or discrete domain, respectively.

The analysis of the linear systems as well as of the signals that interact with the different elements of the system and the environment that surrounds it, requires a clear knowledge of the mathematical analysis and especially of what is known as operational calculation, as of

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