Comparative presentation and visualization of related notions and operations can dissolve possible misconceptions, and enhance comprehension regarding the involved concepts. Applying this rationale, the article describes an attempt to present the essential mathematical transforms applied in signal analysis in a unified manner by making use of concept maps combined with an algorithmic process. The aims of the presentation are on one hand to identify possible cases and sub-cases of the relevant mathematical operations and on the other hand to better illustrate the applicability of each individual operation and the way those operations are associated with each other.

The presented operations include:
(a) phasors and Fourier series,
(b) the Fourier transform,
(c) the Laplace transform and
(d) the z-transform.

All the above operations highlight signals’ representation in frequency-related domains and as such are essential elements of signal theory, yet several students find it difficult to comprehend and properly apply them when it comes to the analysis of particular signals. The difficulty does not only regard the pure mathematical aspect (the algebra involved) but it also concerns the actual meaning and applicability of each operation as well as how those operations are associated with each other. An additional difficulty is that the above operations are usually presented within different courses (often, at different study periods) so the students do not have the opportunity to encounter them in a unified “horizontal” manner.

The concept map involves complementary perspectives including:
a) the low-level arithmetic operations (formulas and computational methods),
b) the high-level objectives of applying these transformations related to possible applications or problems to resolve,
c) the selection criteria, the characteristics, the semantics and the restrictions of the original and transformed signal.

The key concepts and their relationships are described and visualized in an ontology-inspired approach.

The presentation took place during a two-teaching-hour lecture in the framework of the 5th-semester “Telecommunication Systems” course offered at the Dept. of Electrical & Electronic Engineering Educators of the School of Pedagogical & Technological Education (ASPETE), Athens, Greece. The graduates of the School have the option to be employed as teachers in technological secondary education so it is essential for them to develop conceptual (not only procedural) understanding of the various topics of their studies. Prior to the above course, the students had encountered the relevant operations in the framework of separate courses.

Active participation of students (necessary, in any case, due to the teaching-time restrictions) mainly anticipated the revision of the basics of the mathematical operations involved as taught in previous separate courses. The outcome of the procedure was evaluated by means of a short questionnaire (distributed to the students following the lecture) that should be answered on the basis of a 5-grade Likert scale. The questionnaire was formed in such a way as to facilitate the comparison between students’ degree of comprehension prior and after the presentation of the operations mentioned.

Keywords: Engineering Education, Electrical Engineering Education, Electronic Engineering Education, Signal Analysis, Mathematical Transforms, Concept Maps.