Random signals processing
Download in PDF- Lecturer: Kieu NGO (kieu.ngo@sorbonne-universite.fr)
- Course code: UM4EET12
- Student workload: 12h of lectures, 10h of tutorials, 6h of labs
- Credits: 3 ECTS
- Specialization tracks:
- Semester offered: S1 S2 S3 S4
- Language of instruction: French English
- Targeted audience: Eng. Sc. department Other :
- Localization : PMC Campus Other :
Course Overview
The objective of this course is to introduce solid bases on the fundamental concepts and tools of random signal processing since most signals of interest in physics and engineering have a random component (notion of noise). After a reminder on the probabilities which is essential for the understanding of the course, we will introduce random variables and random processes. Several tools for the characterization and analysis (mathematical expectation, variance, power spectral density...) as well as the detection, filtering and estimation of random signals will be introduced.
Mots-clés : Probability, Random signals, Stationnarity, Moments, Ergodicity, Prediction, Power spectral Density
Prerequisites
Students should have previously acquired the following prerequisites to follow this course:
- Basics of signals and systems, notions of probabilities
- Basics of analog and digital electronics
- Basics of deterministic signal processing (usual transforms, spectral analysis, correlation, and convolution)
Intended Learning Outcomes
By the end of this course, students will be able to:
- Characterizing and analyzing random signals in the time domain as well as in the frequency domain
- Proposing a linear model of prediction for random signals
- Determining the characteristics of random signals after filtering
- Deciding if a specific signal is present or not (simple detection) and in which category a signal belongs (multiple detection)
Indicative Teaching Sequence and Methods
| Week | C/TD/TP* | Content | Preparation | Learn.\ outc. |
|---|---|---|---|---|
| S1 | C1 | Basics of probabilities | ||
| S2 | C2 | Moments of ordrer 1 and order 2 | AAV1 | |
| S3 | C3 | Stationnarity | AAV1 | |
| S4 | TD1 | Probability | ||
| S5 | C4 | Prediction, Intercorrelation | AAV2 | |
| S6 | TD2 | Moments, Stationnarity, Prediction | ||
| S7 | ER1 | |||
| S8 | C5 | Ergodicity, Filtering, Spectral analysis | AAV3 | |
| S9 | TD3 | Autocorrelation, ergodicity, Stationnarity | ||
| S10 | C6 | White noise, Power sepectral density, Detection | AAV3+AAV4 | |
| S11 | TP1 | Anaysis of random signals, Prediction | ||
| S12 | TD4 | PSD, filtering | ||
| S13 | TD5 | Filtering, detection | ||
| S14 | TP2 |
- C/TD/TP respectively corresponds to lectures, tutorials and lab sessions.
Indicative Assessment of Intended Learning Outcomes (1st session)
| Week | Individ./group | In-person/remote | Type of exam | Evaluated outcomes | Scale % |
|---|---|---|---|---|---|
| S7 | Collective | In-person | Written | 40% | |
| S15 | Collective | In-person | Written | 45% | |
| S15 | Collective | In-person | Practical | 15% |
2nde session
| Session | Individ./group | In-person/remote | Type of exam | Evaluated outcomes | Scale % |
|---|---|---|---|---|---|
| 2 | Collective | In-person | Written | 85% | |
| 1 | Collective | In-person | Practical | 15% |
Bibliographic references
- Frédéric de Coulon, Théorie et Traitement des signaux, Edition Dunod, 1984
- Hwei Piao Hsu, Signaux et communications, Série Schaum, Édiscience , Dunod, 2004
- Charbit, Eléments de théorie du signal : aspects signaux aléatoires, Ellipses, 1996
- Shaila Dinkar Apte, Random Signal Processing, CRC Press, 2017
Date of generation of this unit description: 14/01/2026
