AN EXAMPLE-BASED, UNIFIED PRESENTATION OF FOURIER ANALYSIS TO UNDERGRADUATE ELECTRONIC ENGINEERING STUDENTS
1 School of Pedagogical & Technological Education (ASPETE) (GREECE)
2 National Technical University of Athens (GREECE)
3 University of West Attica (GREECE)
About this paper:
Conference name: 15th International Technology, Education and Development Conference
Dates: 8-9 March, 2021
Location: Online Conference
Abstract:Fourier analysis is an essential tool for electronic engineers, which, however, undergraduate students find it difficult to comprehend (even when they have the required mathematical background) and in most cases fail to obtain the necessary insight into the physical meaning of the associated definitions and properties.
The article describes a presentation of Fourier analysis which, instead of the conventional approach, is based on two particular example signals, the rectangular pulse train (for Fourier series) and the rectangular pulse (for Fourier transform). Apart from being essential for digital transmission, those two signals involve relatively simple calculations and make it easier to present basic facts and properties of Fourier analysis including relation between trigonometric and complex series, transition from Fourier series to Fourier transform, frequency shift and modulation, inter-relation between signal’s duration, bit-rate and bandwidth, even derivation of Fourier coefficients and transform for other signals such as the unit impulse / unit impulse train and the triangular signal.
Presentation included 6 teaching hours of lecture and relevant discussions. To enhance outcome the students were actively involved in the teaching process. The students had access to selected introductory material in advance before attending the first 2-hour lesson, where the basic facts of Fourier analysis were explained based on the rectangular pulse train and the rectangular pulse. Then, they were given a set of assignments that included manual calculations as well as questions to help them get the necessary insight into the physical aspects of Fourier analysis. Students were encouraged to search through the Internet for demonstrations regarding synthesis of pulse-train signals by means of their frequency components. The second 2-hour session included a discussion on the assignments and the students’ answers. The last 2-hour lecture concluded Fourier analysis including presentation of non-telecom applications (e.g. periodic gratings) in order the students view Fourier method in a more unified manner. Inclusion of non-telecom applications was considered necessary since, in the previous years, most students were unable to associate Fourier series (as presented in mathematics courses) with Fourier analysis of periodic signals. The last lecture was followed by a final set of assignments (given together with guiding material) that also included optional exercises on other telecom signals as well as non-telecom applications.
The described approach was applied to a class of 75 5th-semester students at the Electrical & Electronic Engineering Educators Dept. of the School for Pedagogical & Technological Education (ASPETE), Athens, Greece in the framework of an introductory course on telecommunication systems. Graduates of ASPETE may be employed as teachers at technological high schools so comprehension of basic engineering concepts and procedures is essential for them. The evaluation included a short exam (to test students’ knowledge on basic mathematical and physical aspects of Fourier analysis) and a questionnaire (to have their attitude on the applied approach). Results were encouraging with about 70% of students getting a passing grade (a much better performance than the course’s passing rate of previous years) and almost all students having a favorable attitude towards example-based analysis as compared to a more formal one.
Keywords: Engineering Education, Electronic Engineering Education, Telecommunications.