Courses

Transform Theory and Systems

General

Course Contents

Signals and Systems: definitions, classification, types of representation. The complex Fourier Series and the Fourier Transform. The Discrete Time and the Discrete Fourier Transform. Basic system properties: linearity, time invariance, causality, stability. Impulse and step response of a system, convolution. Difference equations and differential equations. Analysis of signals and systems in frequency domain. Spectral representation:
magnitude and phase diagrams. Frequency response. Frequency selection filters. Laplace Transform and z-Transform. Transfer function. Pole-zero diagrams. Connecting LTI systems: parallel, cascade and feedback connection. The Nyquist–Shannon sampling theorem. Pulse Width Modulation. Design and implementation of discrete time systems with block diagrams. Parameter accuracy. Applications and examples.

Educational Goals

The course is designed as an introduction to the basic concepts of analysis and synthesis of linear systems, using the mathematical tools provided by the theory of transformations. On completion of the course, students should be able to:
(a) recognize the basic properties of systems and apply them when solving problems;
(b) interpret and process mathematically, both in time domain and in frequency domain (spectrum), the characteristics of analog and discrete signals as well as the characteristics of linear and time invariant (LTI) systems;
(c) draw the pole-zero diagram of the transfer function of an LTI system and analyze the effect of their position;
(d) calculate the output of an LTI system (for a given input) both in time and frequency domains, by using the appropriate transformations;
(e) model problems of different fields of science (engineering, economics, etc.) through linear and time-varying systems and to analyze them in time and frequency;
(f) formulate the sampling theorem as well as its consequences and apply it to the solution of signal and simple discrete system problems;
(g) interpret the discrepancies between the predicted and measurable behavior of the discrete systems; and
(h) attend, without significant gaps, more specialized industrial engineering and management courses.

General Skills

Research, analysis and synthesis of data and information, using corresponding technologies, Adaptation to new situations, Decision making, Working in an international environment, Independent work, Teamwork – distribution of responsibilities, Working in an interdisciplinary environment, Practicing criticism and self-criticism, Promoting free, creative and inductive thinking.

Teaching Methods

Lectures, Exercises, Online guidance, Projected Presentations, E-mail communication, Online Synchronous and Asynchronous Teaching Platform (moodle).

Students Evaluation

Assessment Language: English / Greek
The grade of the course is formed 100% by a written final examination including problem solving, graphs, diagrams and calculations based on data.

Recommended Bibliography

Signals and Systems – 2nd E, Oppenheim, Willsky, Nawab, ISBN 0-13-814757-4.
Signals, Systems and Transforms,4th E, CHARLES L. PHILLIPS , JOHN M. PARR, EVE A. RISKIN, ISBN-13: 978-0-13-198923-8.
Signal Processing & Linear Systems, 2nd E, B.P. Lathi, ISBN-13: 978-0195158335.