Conceptual understanding of complex components and Nyquist-Shannon sampling theorem: A design based research in Engineering

Abstract

The ubiquity of complex components and variables is well-known in all fields of engineering. The didactic importance of complex numbers and Euler's formula is emphasized by this fact. Students express the topic to be difficult to comprehend and “imaginary”. So to present this topic in an appropriate and student-centered way is of great challenge for each lecturer. In this paper the Euler's Formula is also applied for explaining and for understanding the aliasing effect when it occurs in the reconstruction of sampled signals. The fundamental target of this contribution is to overcome barriers in student's understanding and, in doing so, to improve the quality of engineering education. Guided by this objective a design-based research was carried out. Theory-based new didactic approaches have been developed in order to increase student's conceptual understanding of complex arithmetic. In addition, new theoretical insights into the comprehension problems are gained. The research design, the intervention developed and the empirical findings will be presented.