The Role of Fourier Series in Mathematics and in Signal Theory

Abstract

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.