# Signal processing

LELEC2900  2019-2020  Louvain-la-Neuve

Signal processing
5.0 credits
30.0 h + 30.0 h
2q

Teacher(s)
Language
Anglais
Aims

• 1

With respect to the AA referring system defined for the Master in Electrical Engineering, the course contributes to the develoopment, 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”.

Content
• 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
• Theory of multiresolution and wavelet transforms: links between sampling and projection on a vector space generated by orthonormal basic functions of index type. Examplification by the Haar Transform.
• Compressive sensing.
• Exercises on the use of Python for the prototyping of signal processing systems
Teaching methods

14 lectures

12 training sessions

Evaluation methods
• 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).
Online resources
Bibliography
• Syllabus de cours disponible sur Moodle
• Transparents et articles de référence disponibles sur Moodle
• Enregistrement de la 1ère moitié du cours, disponible en podcast

Lectures notes on Moodle

Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Program title
Sigle
Credits
Prerequisites
Aims
Master [120] in Biomedical Engineering
5
-

Master [120] in Electrical Engineering
5
-

Master [120] in Mathematical Engineering
5
-