In part I of this paper, 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 this paper, the development of all the transforms that are studied in the Signals and Systems courses is presented, starting from the Discrete Fourier Transform until reaching the Z Transform, passing through the Fourier Series, the Fourier Transform, the Laplace transform, etc. The methodology used consists of constructing the Discrete Fourier Transform in a didactic way, to then deduce all the other entities by using the infinitesimal calculus.

中文翻译：

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信号和线性系统：一种基于无穷微积分的新颖方法（第一部分）

在本文的第一部分中，基于无限微积分模型MicroCalculus，介绍了有关线性信号和系统的课程的开发。这种演算模型允许对信号过程的基本概念进行有说服力的开发。信号由变量和函数的基本元素定义。MicroCalculus为信号分类提供了新视野，并将非标准函数视为通用函数，在新的演算模型中可以将其视为标准函数。然后，从统一的角度介绍了离散和连续卷积运算的发展。在本文的第二部分中，介绍了在“信号与系统”课程中研究的所有变换的开发，