This paper presents a praxeological analysis, based on ATD (Anthropological Theory of the Didactic), of the topic of Fourier series, as this topic is introduced and used in mathematics and in electrical engineering, more precisely in signal theory. The analysis is based mainly on one widely used textbook in mathematics for engineers, and a textbook and video lectures in signal theory. The aim of the analysis is to investigate possible differences in the motivation for introducing Fourier series in mathematics and in signal theory, as well as differences in the techniques used, and the justifications behind the techniques. This research is inspired by previous research showing lack of connection between mathematics courses and engineering courses applying mathematics. To get a wider perspective, the exposition in the textbook in mathematics for engineers is also compared to the exposition in more advanced books in mathematics. To add to the perspective, the historical origin of Fourier series is also discussed. The findings show that there are differences in the motivation for the topic both between mathematics and signal theory, but also between basic and more advanced mathematics. Within mathematics there are also differences in the underlying theories.

本文基于 ATD（教学人类学理论）对傅立叶级数主题进行了行为学分析，因为该主题在数学和电气工程中被引入和使用，更准确地说是在信号理论中。分析主要基于一本广泛使用的工程师数学教科书，以及一本信号理论教科书和视频讲座。分析的目的是调查在数学和信号理论中引入傅立叶级数的动机可能存在的差异，以及所用技术的差异以及这些技术背后的理由。这项研究的灵感来自先前的研究，该研究表明数学课程和应用数学的工程课程之间缺乏联系。为了获得更广阔的视野，工程师数学教科书中的说明也与更高级的数学书籍中的说明进行了比较。为了增加视角，还讨论了傅立叶级数的历史起源。研究结果表明，数学和信号理论之间以及基础数学和更高级数学之间的主题动机存在差异。在数学内部，基础理论也存在差异。