Signals and Linear Systems: A Teaching Approach Based on Infinitesimal Calculus (Part I)
Keywords:e-learning, signals and systems, Educational technology
In this article, part I of II, the development of a course on linear signals and systems is presented, based on an infinitesimal calculus model, called MicroCalculus. Such a calculus model allows a didactic development of the fundamental concepts of a signal course. The signals are defined from the
fundamental elements of variable and function. MicroCalculus offers a new vision to signal classification, as well as a treatment of non-standard functions as generalized functions, which in the new calculus model can be treated as standard functions. Then, the development of the discrete and continuous convolution operation is presented, from a unified approach.
In part II of the article, the solution of the differential equations of linear systems using infinitesimal calculus is presented. Then, a unified development of the Fourier Analysis is performed, where the Fourier Series, the Transform and the Discrete Transform are presented as 3 versions of the same entity. Finally, a didactic development of the Discrete Fourier Transform is presented.