
Σήματα και Συστήματα
 Title:  Σήματα και Συστήματα  Lesson Code:  3215502  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 noncausal systems, linear and nonlinear 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  It is the intent of this course that students will:
1. be able to describe signals mathematically and understand how to perform mathematical operations on signals.
2. be familiar with commonly used signals such as the unit step, impulse function, sinusoidal signals and complex exponentials, and be able to classify signals as continuoustime or discretetime, as periodic or nonperiodic, as having even or odd symmetry.
3. be able to describe linear time invariant systems either using differential equations or using their impulse response.
4. understand various system properties such as linearity, time invariance, causality, boundedinput boundedoutput stability and be able to identify whether a given system exhibits these properties and its implication for practical systems.
5. understand the process of convolution between signals, its implication for analysis of linear time invariant systems and the notion of an impulse response.
6. be able to solve linear differential equations using Laplace transform techniques.
7. understand the intuitive meaning of frequency domain and the importance of analyzing and processing signals in the frequency domain.
8. be able to compute the Fourier series or Fourier transform (and its inverse) of various signals.
9. understand the application of Fourier analysis to ideal filtering, amplitude modulation and sampling.
10. be able to process continuoustime signals by first sampling and then processing the sampled signal in discretetime.
11. develop basic problem solving skills and become familiar with formulating a mathematical problem from a general problem statement.
12. be able to use basic mathematics including calculus, complex variables and algebra for the analysis and design of linear time invariant systems used in engineering.
13. develop a facility with MATLAB programming to solve linear systems and signal problems.   Prerequisites  Calculus
Linear algebra
Circuit theory   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.   Additional References  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
Activity/Workload
Lectures: 39 hrs
Lab practice: 8 hrs
Lab assignments: 20 hrs
Personal study: 60 hrs
Final exam: 3 hrs
Total: 130 hrs (5 ECTS)   Assessment/Grading Methods  Lab exercises (30%), written examination (70%).   Language of Instruction  Greek, English (for Erasmus students)   Μode of delivery  Weekly class meetings
Lab practice (4 sessions per semester) 

