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Signals and Systems

 Title: Signals and Systems Lesson Code: 321-5502 Semester: 3 ECTS: 5 Theory Hours: 3 Lab Hours: 2 Faculty: Leros Asimakis

Content outline

Basic definitions of signals and systems, periodic signals, unit step, impulse function. Systems’ categories, static and dynamic systems, causal and non-causal systems, linear and non-linear systems, time invariant and variant systems. Impulse response of linear systems. Convolution properties. Systems’ stability. Fourier Transform (FT) and inverse FT. Convergence and properties of FT. Application of FT to the study of linear systems, system’s frequency response, description of Linear Time Invariant (LTI) systems with differential equations and the FT, ideal lowpass filter. Fourier series, Fourier series of periodic functions, Fourier series for even or odd symmetry, Parseval’s theorem. Laplace transform, properties and theorems. Inverse Laplace transform. Relation of the Laplace and Fourier transforms. Bilateral Laplace transform. Use of the Laplace transform in the solution of linear differential equations. Use of the Laplace transform in the analysis of linear systems and the study of their stability. State space, state, observability, controllability. Signal and systems of discrete time. Z transform and its properties, inverse Z transform. FT of discrete time. Unilateral Z transform. Sampling – Nyquist’s theorem. Discrete Fourier Transform (DFT).

Learning outcomes

Upon completing the course, students will be able to:

• distinguish between systems and models, and understand their interrelation
• understand basic system properties such as linearity, causality, stability etc
• use basic exponential, trigonometric and generalized functions to represent physical signals
• describe the relation between systems and signals by mathematical tools such as differential equations, difference equations, convolution, frequency response etc
• compute the output signal from the input signal and the system's mathematical model
• mathematically describe the interconnection of systems
• understand the analysis and processing of signals in the frequency domain
• understand the sampling process and the relation between discrete-time signals and their continuous-time counterparts
• use Matlab fr problem solving

Basic Textbooks

1. Θεοδωρίδης Σέργιος, Μπερμπερίδης Κώστας, Κοφίδης Λευτέρης, Εισαγωγή στη θεωρία σημάτων και συστημάτων.
2. Καλουπτσίδης Νίκος, Σήματα, συστήματα και αλγόριθμοι.
3. Σήματα και συστήματα, Oppenheim / Willsky / Nawab.

1. Simon Haykin and Barry Van Veen, Signals and Systems 2005 JustAsk! Edition, John Wiley & Sons, Inc.

Learning Activities and Teaching Methods

Lab exercises

Final written exam

Lectures: 39 hrs

Lab practice: 8 hrs

Lab assignments: 20 hrs
Personal study: 60 hrs
Final exam: 3 hrs
Total: 130 hrs (5 ECTS)

Lectures 39 hours
Laboratory hours 26 hours
Personal study 57 hours

Final exams 3 hours
Course total 125 hours (5 ECTS)

Language of Instruction
Greek, English (for Erasmus students)

Μode of delivery

Weekly class meetings
Lab practice (4 sessions per semester)

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