Implementação computacional para cálculo da convolução de sinais contínuos e discretos no tempo e aplicações

Abstract

The study of signals and systems makes a study field very important for Engineering. It’s through this kind of study that it’s possible to model, represent, study and understand various phenomena that occurs in peoples day life. The present paper intends to study an important type of systems, the Causal Linear Invariant Time Systems, as it will also work through the continuous and discrete time signals. An important mathematics operation and largely used in the study of signals and systems is the convolution, which will be studied and It will be presented a new way to compute it. Therefore, the main goal for this paper is to implement in computer software an algorithm that solves the convolution for exponential signals, continuous and discrete in time, without using convolution integrals and summation, but using linear systems resolution based in Vandermonde matrices. For that, the specific goals for the study are to understand the basic theory about signals and systems and the convolution calculation method that will be used, implement a software algorithm to execute the convolution calculation method studied and to search for problems about analog circuits and digital filters that could be used to test the code implemented. Therefore, It was made a bibliographic research aiming to understand the main concepts and to search problems for application, as well for the software implementation It was used the Scilab® software package to develop the algorithm. In this way, the code was used to help solve and understand a problem about a parallel RLC circuit and a fourth order Chebyshev Digital Filter, where It was knew the equations for the systems and we looked for the impulse response e the system solution for some kinds of input signals. Ultimately, It was possible to see the algorithm working and helping the study of complex problems as It was expected, turning to an alternative for the exponential signals convolution calculation and in the study of systems.