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| SYST0002-2 | Modelling and analysis of systems
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| Duration : | 30h Th, 30h Pr, 15h Proj. |
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| Number of credits : |
| Bachelor in engineering (Bachelor in engineering sciences, civil engineer orientation), 3rd year | | 5 |
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| Master in Aerospace Engineering, research focus, 1st year | | 5 |
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| Master in Engineering Physics, research focus, 1st year | | 5 |
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| Master in Aerospace Engineering, Professional Focus (Management), 1st year | | 5 |
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| Master in Engineering Physics, specialized approach, 1st year | | 5 |
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| Master in Computer science | | 6 |
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| Master in Mathematical Sciences, professional focus in computer science, 2nd year | | 6 |
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| Lecturer : | Rodolphe Sepulchre |
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| Substitute(s) : | Erik Quaeghebeur |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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- Systems and signals: discrete vs. continuous, basic definitions, properties, and examples
- State space models
- Input-output models
- Linear Time-Invariant or LTI systems: convolutional and (A,B,C,D) models
- Fourier series: Frequency decomposition of periodic signals
- Signal transforms: the Fourier transforms, Laplace transform, and z transform
- Analysis of LTI systems using the Laplace and z transforms
- LTI system stability and transient/steady-state responses
- Frequency response of LTI systems
- Fourier transforms of periodic signals
- Applications of Fourier transforms: windowing and sampling
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Learning outcomes of the course :
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- Being able to give standard mathematical formulations of signals and systems, both in continuous and discrete time, and both in the context of input-output and state-space models
- Recognizing important simplifying system properties or applying them as model assumptions: linearity, time invariance
- Being able to derive practically important signal and system properties: static vs. dynamic, stability, causality
- Being able to use the mathematical techniques of convolution, Fourier series decomposition, Fourier transforms, and Laplace / z transforms to analyze LTI systems
- Being able to work with idealized signals (impulses, steps, complex exponentials) for the analysis of systems: impulse and step response, transfer function frequency response
- Being able to take into account initial conditions in the analysis of LTI systems
- Being capable of working both in the temporal and frequency domain and of moving between both domains, for example for sampling applications
- Knowing how to represent systems and signals graphically: block diagrams, signal graphs, Bode plots, complex plane representations of properties of transfer functions
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Required: the following ULg courses, or equivalent ones,
- Analyse mathématique 1 and 2 (MATH0002 and MATH0502)
- Algèbre (MATH0013)
- Physique 1 (PHYS2020)
Recommended:
(given that the theory courses are thought in English) |
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Planned learning activities and teaching methods :
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- Theory courses to introduce and illustrate the concepts and techniques that form the course's subject matter; ex cathedra
- Practical exercices to practice essential mathematical and modelling techniques required for attaining the learning outcomes; supervised individual work
- A programming project to use the techniques learned in a more concrete context; individual work, but problem discussion within the student group is encouraged
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Mode of delivery (face-to-face ; distance-learning) :
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- Theory course: plenary, in English
- Practical exercises: in groups, in French
- Project: individually, in French
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Recommended or required readings :
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| Required:
- Course notes, in French
- Exercise syllabus, in French
Recommended:
Students are encouraged to actively and independently look for and consult books and other material, also on-line, to supplement the required material and give them a broader view of the subject area. |
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Assessment methods and criteria :
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| Evaluations:
- One written test during the semester
- One individual programming project with a written report during the semester
- The exam is written and closed book
The test and exam will consist of exercises to be solved, which may vary from theoretical to more practical in nature.
Evaluation criteria:
- explicitly apparent achievment of the learning outcomes (understanding of concepts, mastering of techniques),
- creative combination of individual concepts and techniques, i.e., going beyond plain repetition of definitions and application of formulas
- arithmetic and mathematical correctness,
- clarity of responses.
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| E. Quaeghebeur
R. Liégeois |
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| Items online : |
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| Course website |
| Information about the schedule, classrooms, and projects can be found on the course website |
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