Duration
26h Th, 26h Pr, 15h Proj.
Number of credits
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
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. It will 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 and discrete 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 and Z transforms, 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. An exhaustive description of the course is available at http://sites.google.com/site/gdrion25/teaching/syst0002
Learning outcomes of the learning unit
At the end of the course, the student will be able to
- master the notions of analog and digital 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 or discrete 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 and Z 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.
- sample continuous signals, and reconstruct a continuous signal from its samples.
- Master Shannon/Nyquist theorem and the notion of aliasing.
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 11 lectures on theoretical concepts and applications and 10 tutorials.
For more informations, see the course webpage:
http://sites.google.com/site/gdrion25/teaching/syst0002
Mode of delivery (face-to-face ; distance-learning)
Face-to-face.
Recommended or required readings
Slides will be available on the course webpage along the year.
Textbooks on theory and tutorials are also available on the webpage, and printed versions can be bought at the CdC.
Other useful references:
"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.
Assessment methods and criteria
Four short facultative assignments during the year and a written exam (theory + exercices) at the end of the semester.
Work placement(s)
Organizational remarks
Detailed informations about the organisation of the course are provided on the course webpage
http://sites.google.com/site/gdrion25/teaching/syst0002
Contacts
G. Drion (gdrion@ulg.ac.be, Bat. B28, bureau I140).
Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session
Teaching methods implemented : distance-learning
Assessment subjects
Assessment methods
Contacts
Adaptation of teaching commitments following the COVID-19 pandemic for the Aug-Sept 2020 session
Assessment subjects
The assessment will be about all the topics covered during the lectures and the tutorials as in January.
Assessment methods
The assessment will be organized as an open-book online test on eCampus. The test will be made available according to the date and time provided for in the examination schedule. Students will need to complete the test within the set deadlines. The test will mainly consist of true/false questions, multiple choice questions, numeric questions, and short answer questions.
Contacts
G. Drion (gdrion@ulg.ac.be, Bat. B28, bureau I140).