Signal processing

5.00 credits

30.0 h + 30.0 h

Teacher(s)

Jacques Laurent; Vandendorpe Luc;

Language

English

Learning outcomes

At the end of this learning unit, the student is able to :
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”.

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
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. 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

First half of the course available as a podcast

Faculty or entity

ELEC

Title of the programme

Sigle

Credits

Prerequisites

Learning outcomes

Master [120] in Electrical Engineering

ELEC2M

Master [120] in Biomedical Engineering

GBIO2M

Master [120] in Mathematical Engineering

MAP2M