2023-2024 / SYST0002-2

Introduction to signals and systems

Duration

26h Th, 26h Pr, 15h Proj.

Number of credits

 Bachelor of Science (BSc) in Engineering5 crédits 
 Master of Science (MSc) in Aerospace Engineering5 crédits 
 Master of Science (MSc) in Computer Science and Engineering (double degree programme with HEC)5 crédits 

Lecturer

Guillaume Drion

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course introduces the basic concepts of signal and system analysis and representation in continuous time. It will start by presenting geometric tool for nonlinear systems analysis, and then focus on the methods developed for linear, time-invariant (LTI) systems. The course is constructed upon two complementary approaches for the representation of signals and systems: the state-space approach and the input-output approach. It is composed of three main themes:









  • Modeling - The "modeling" part introduces methods for the mathematical representation of dynamical systems in continuous time. It illustrates the use of these methods through examples from engineering, including example from mechanical engineering, electrical engineering, chemical engineering and biomedical engineering. On the one hand, this part introduces the general structure of state-space models, the notions of parameters and variables, equilibrium and stability, linearity and methods to linearize a system around an equilibrium point. On the other hand, it introduces the notions of input-output representation in the time domain (impusle response, convolution, etc.) and in the frequency domain (complex exponential, Laplace, etc.). 
  • Analysis - The "analysis" part introduces the analysis methods developed for signals and systems in the case of linear, time-invariant systems.
    The part "signal analysis" defines the basic concepts of signals encountered in engineering (causality, periodicity, etc.). It introduces the structure and properties of specific signals (Dirac delta function, step function, ramp function, complex exponential, etc.). It intoduces the concepts of spectral decomposition of a signal, Fourier series and Fourier transforms.
    The "systems analysis" part describes how to extract the basic properties of a dynamical system such as stability, linearity, time-invariance, causality, etc. from their state-space and input-output representations.In particular, it introduces the tools to analyze the dynamical properties of a LTI system from its impulse response (causality, time constant and bandwidth, memory, etc.) and from its transfer function (poles and zeros, zero-input and zero-state responses, Laplace and Z transforms, frequency response and Bode plots, etc.).
  • Design - The "design" part uses the modeling and analysis methods described above for the development of systems generating basic operations on signals. In particular, it will focus on sampling and windowing methods. This part will aslo include the design principles of dynamical systems (systems interconnection, feedback systems, etc.). 
 

The different part of the course will be motivated by examples from engineering.

Learning outcomes of the learning unit

At the end of the course, the student will be able to








  • master the notions of analog signals, basic operations on signals, the structure and properties of the Dirac Delta function, the step function, the complex exponential. 
  • master the concepts of static and dynamical systems, state-space representation, parameters and state variables, linearity and time-invariance.
  • construct a state-space representation of a dynamical system in continuous time, analyze its properties, compute its equilibrium points and their stability, linearize a nonlinear system around an equilibrium point. 
  • compute the convolution of two signals (continuous and discrete).
  • master the concept of input-output representation of systems, the superposition principle and the specific case of linear-time invariant (LTI) systems.
  • compute the input-output reponse of an LTI system in time domain (impulse and step responses), analyze the systems properties on the basis of its impulse response.
  • master the concepts of spectral decomposition of signals, compute the Fourier series and Fourier transforms of continuous and discrete signals. 
  • master the concepts of Laplace transform (inculding the regions of convergence) and compute the input-output response of a LTI system in the frequency domain (transfer function). 
  • analyze systems basic propeties on the basis of its transfer function (pole, zeros, static gain, etc.).
  • analyze a systems response from its frequency response, plot and interpret the Bode plots.
  • reproduce the canonical form of the transfer function and time response of 1st and 2nd order systems.
  • link the temporal and frequency responses of LTI systems. 
This course contributes to the learning outcomes I.1, II.1, III.1, III.2, VI.1, VII.2, VII.4, VII.5 of the BSc in engineering.

Prerequisite knowledge and skills

An introductory course on linear algebra and calculus. Basic knowledge in mechanics and electrical circuits is also useful. 

Planned learning activities and teaching methods

The course is based on 10 lectures on theoretical concepts and applications and 10 tutorials.

Mode of delivery (face to face, distance learning, hybrid learning)

One virtual session, the others in face-to-face (see online schedule).

Recommended or required readings

Slides and ipad notes will be available on the course webpage along the year.
ThetTutorials textbook is also available on the webpage.
Other useful references:  "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering", Steven Strogatz. "Signals and Systems (2nd Edition)", Alan V. Oppenheim and Alan S. Willsky.  "Structure and interpretation of signals and systems", Lee and Varaiya. "Analog and Digital Signal Processing", Ambardar.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )


Additional information:

A written exam (theory + exercices) at the end of the semester.

Work placement(s)

Organisational remarks and main changes to the course

Informations and documents will be available on the eCampus and myUliege platforms. 

Contacts

G. Drion (gdrion@ulg.ac.be, Bat. B28, bureau I140).

Association of one or more MOOCs

Items online

TP2 - 1D NL systems
Theoretical summary and exercise solved on the blackboard for the practical exercice session on 04/10/23