Signal processing

5.00 crédits

30.0 h + 30.0 h

Enseignants

Jacques Laurent; Vandendorpe Luc;

Langue
d'enseignement

Anglais

Acquis
d'apprentissage

A la fin de cette unité d’enseignement, l’étudiant est capable de :
1	At the end of this learning unit, the student is able to : With respect to the AA referring system defined for the Master in Electrical Engineering, the course contributes to the development, mastery and assessment of the following skills : AA1.1, AA1.2, AA1.3 AA2.1, AA2.2 AA6.1 The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

Contenu

Sampling: theorem, interpolation, sequence
Sampling rate change: downsampling and interpolation for low-pass signals and bandpass signals, complex envelope
Processing structures and graph theory: switching, transposition, direct and polyphase structures
Discrete Fourier transform, properties, convolution, truncation and window
Finite impulse response filters, phase linearity, types and properties of poles and zeros
Synthesis of FIR filters: window method, frequency response sampling, minimax synthesis and Remez method
Synthesis of IIR filters: Prony method, synthesis method by bilinear transformation
Comparison of the IIR and FIR filters: discussion on the linear phase and the complexity
Non-parametric spectral analysis by the discrete Fourier transform: compromise between the resolution and the level of the secondary lobes
Fast Fourier Transform (FFT) algorithm
Parametric spectral analysis: identification of a auto regressive model - Yule-Walker equation and Levinson-Durbin algorithm
Adapted and adaptive filtering.
Theory of multiresolution and wavelet transforms: links between sampling and projection on a vector space generated by orthonormal basic functions of index type. Example of the Haar Transform.
Compressive sensing : principles and algorithms.
Exercises on the use of Python for the prototyping of signal processing systems

Méthodes d'enseignement

14 lectures
12 training sessions

Modes d'évaluation
des acquis des étudiants

Concerning the lectures, the students are individually evaluated with a written exam, including problems solving, and questions on the theory.
For the numerical exercises on Python, the students are evaluated in computer room (in-session or out-of-session).

Ressources
en ligne

Bibliographie

First half of the course available as a podcast

Faculté ou entité
en charge

ELEC

Intitulé du programme

Sigle

Crédits

Prérequis

Acquis
d'apprentissage

Master [120] : ingénieur civil électricien

ELEC2M

Master [120] : ingénieur civil biomédical

GBIO2M

Master [120] : ingénieur civil en mathématiques appliquées

MAP2M